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THE TRIANGLE AND ITS PROPERTIES

298387 The sides of a right triangle containing the right angle are (5x)cm and (3x-1)cm. If area of triangle be 60cm $^{1}$ , calculate the length of the sides of the triangle.

1 15cm, 8cm, 17cm

2 16cm, 8cm, 17cm

3 16cm, 8cm, 19cm

4 18cm, 8cm, 14cm

Explanation:

15cm, 8cm, 17cm
Given: In a right angled triangle, Perpendicular = 5x and Base = 3x - 1
Area = 60cm $^{1}$
Area of triangle $= \frac{1}{2}$ ?(base)(height)
$60 = \frac{1}{2} (5 x) (3 x - 1)$
120 = 15x $^{1}$ - 5x
24 = 3x $^{1}$ - x
3x $^{1}$ - x - 24 = 0
3x $^{1}$ - 9x + 8x - 24 = 0
3x (x - 3) + 8(x - 3) = 0
(3x + 8)(x - 3) = 0
$x = 3, \frac{- 8}{3}$
Neglect the nagative value, x = 3
Thus, perpendicular = 15cm and base = 8cm
Now, from Pythagoras theorem,
H $^{1}$ = P $^{1}$ + B $^{1}$
H $^{1}$ = 15 $^{1}$ + 8 $^{1}$
H $^{1}$ = 225 + 64
H $^{1}$ = 289
H = 17cm

THE TRIANGLE AND ITS PROPERTIES

298389 Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion (A): If the altitudes from two vertices of a triangle to the opposite sides are equal, then the triangle is an isosceles triangle.
Reason (R): If two angles and one side of one triangle are equal to two angles and the corresponding side of the other triangle, then the two triangles are congruent.

1 Both A and R are true and R is the correct explanation of A.

2 Both A and R are true but R is not the correct explanation of A.

3 A is true but R is false.

4 A is false but R is true.

THE TRIANGLE AND ITS PROPERTIES

298390 By which of the following criterion two triangles cannot be proved congruent?

1 AAA.

2 SSS.

3 SAS.

4 ASA.

THE TRIANGLE AND ITS PROPERTIES

298391 Which is the longest side in the triangle PQR right angled at P?

1 PQ

2 QR

3 PR

4 None of these

THE TRIANGLE AND ITS PROPERTIES

298392 In a right-angled triangle, the angles other than the right angle are:

1 Obtuse.

2 Right.

3 Acute.

4 Straight.

Explanation:

Acute.
In right angled $△ ABC,$ $∠ B = 90^{\circ}$ [angle sum property of a triangle]
$∠ A + ∠ B + ∠ C = 180^{\circ}$
9
$\Rightarrow ∠ A + 90^{\circ} + ∠ C = 180^{\circ}$
$\Rightarrow ∠ A + ∠ C = 180^{\circ} - 90^{\circ} = 90^{\circ}$
Hence, in a right angled triangle, the angles other than the right angle are acute.

THE TRIANGLE AND ITS PROPERTIES

298387 The sides of a right triangle containing the right angle are (5x)cm and (3x-1)cm. If area of triangle be 60cm $^{1}$ , calculate the length of the sides of the triangle.

1 15cm, 8cm, 17cm

2 16cm, 8cm, 17cm

3 16cm, 8cm, 19cm

4 18cm, 8cm, 14cm

Explanation:

15cm, 8cm, 17cm
Given: In a right angled triangle, Perpendicular = 5x and Base = 3x - 1
Area = 60cm $^{1}$
Area of triangle $= \frac{1}{2}$ ?(base)(height)
$60 = \frac{1}{2} (5 x) (3 x - 1)$
120 = 15x $^{1}$ - 5x
24 = 3x $^{1}$ - x
3x $^{1}$ - x - 24 = 0
3x $^{1}$ - 9x + 8x - 24 = 0
3x (x - 3) + 8(x - 3) = 0
(3x + 8)(x - 3) = 0
$x = 3, \frac{- 8}{3}$
Neglect the nagative value, x = 3
Thus, perpendicular = 15cm and base = 8cm
Now, from Pythagoras theorem,
H $^{1}$ = P $^{1}$ + B $^{1}$
H $^{1}$ = 15 $^{1}$ + 8 $^{1}$
H $^{1}$ = 225 + 64
H $^{1}$ = 289
H = 17cm

THE TRIANGLE AND ITS PROPERTIES

298389 Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion (A): If the altitudes from two vertices of a triangle to the opposite sides are equal, then the triangle is an isosceles triangle.
Reason (R): If two angles and one side of one triangle are equal to two angles and the corresponding side of the other triangle, then the two triangles are congruent.

1 Both A and R are true and R is the correct explanation of A.

2 Both A and R are true but R is not the correct explanation of A.

3 A is true but R is false.

4 A is false but R is true.

THE TRIANGLE AND ITS PROPERTIES

298390 By which of the following criterion two triangles cannot be proved congruent?

1 AAA.

2 SSS.

3 SAS.

4 ASA.

THE TRIANGLE AND ITS PROPERTIES

298391 Which is the longest side in the triangle PQR right angled at P?

1 PQ

2 QR

3 PR

4 None of these

THE TRIANGLE AND ITS PROPERTIES

298392 In a right-angled triangle, the angles other than the right angle are:

1 Obtuse.

2 Right.

3 Acute.

4 Straight.

Explanation:

Acute.
In right angled $△ ABC,$ $∠ B = 90^{\circ}$ [angle sum property of a triangle]
$∠ A + ∠ B + ∠ C = 180^{\circ}$
9
$\Rightarrow ∠ A + 90^{\circ} + ∠ C = 180^{\circ}$
$\Rightarrow ∠ A + ∠ C = 180^{\circ} - 90^{\circ} = 90^{\circ}$
Hence, in a right angled triangle, the angles other than the right angle are acute.

THE TRIANGLE AND ITS PROPERTIES

298387 The sides of a right triangle containing the right angle are (5x)cm and (3x-1)cm. If area of triangle be 60cm $^{1}$ , calculate the length of the sides of the triangle.

1 15cm, 8cm, 17cm

2 16cm, 8cm, 17cm

3 16cm, 8cm, 19cm

4 18cm, 8cm, 14cm

Explanation:

15cm, 8cm, 17cm
Given: In a right angled triangle, Perpendicular = 5x and Base = 3x - 1
Area = 60cm $^{1}$
Area of triangle $= \frac{1}{2}$ ?(base)(height)
$60 = \frac{1}{2} (5 x) (3 x - 1)$
120 = 15x $^{1}$ - 5x
24 = 3x $^{1}$ - x
3x $^{1}$ - x - 24 = 0
3x $^{1}$ - 9x + 8x - 24 = 0
3x (x - 3) + 8(x - 3) = 0
(3x + 8)(x - 3) = 0
$x = 3, \frac{- 8}{3}$
Neglect the nagative value, x = 3
Thus, perpendicular = 15cm and base = 8cm
Now, from Pythagoras theorem,
H $^{1}$ = P $^{1}$ + B $^{1}$
H $^{1}$ = 15 $^{1}$ + 8 $^{1}$
H $^{1}$ = 225 + 64
H $^{1}$ = 289
H = 17cm

THE TRIANGLE AND ITS PROPERTIES

298389 Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion (A): If the altitudes from two vertices of a triangle to the opposite sides are equal, then the triangle is an isosceles triangle.
Reason (R): If two angles and one side of one triangle are equal to two angles and the corresponding side of the other triangle, then the two triangles are congruent.

1 Both A and R are true and R is the correct explanation of A.

2 Both A and R are true but R is not the correct explanation of A.

3 A is true but R is false.

4 A is false but R is true.

THE TRIANGLE AND ITS PROPERTIES

298390 By which of the following criterion two triangles cannot be proved congruent?

1 AAA.

2 SSS.

3 SAS.

4 ASA.

THE TRIANGLE AND ITS PROPERTIES

298391 Which is the longest side in the triangle PQR right angled at P?

1 PQ

2 QR

3 PR

4 None of these

THE TRIANGLE AND ITS PROPERTIES

298392 In a right-angled triangle, the angles other than the right angle are:

1 Obtuse.

2 Right.

3 Acute.

4 Straight.

Explanation:

Acute.
In right angled $△ ABC,$ $∠ B = 90^{\circ}$ [angle sum property of a triangle]
$∠ A + ∠ B + ∠ C = 180^{\circ}$
9
$\Rightarrow ∠ A + 90^{\circ} + ∠ C = 180^{\circ}$
$\Rightarrow ∠ A + ∠ C = 180^{\circ} - 90^{\circ} = 90^{\circ}$
Hence, in a right angled triangle, the angles other than the right angle are acute.

THE TRIANGLE AND ITS PROPERTIES

298387 The sides of a right triangle containing the right angle are (5x)cm and (3x-1)cm. If area of triangle be 60cm $^{1}$ , calculate the length of the sides of the triangle.

1 15cm, 8cm, 17cm

2 16cm, 8cm, 17cm

3 16cm, 8cm, 19cm

4 18cm, 8cm, 14cm

Explanation:

15cm, 8cm, 17cm
Given: In a right angled triangle, Perpendicular = 5x and Base = 3x - 1
Area = 60cm $^{1}$
Area of triangle $= \frac{1}{2}$ ?(base)(height)
$60 = \frac{1}{2} (5 x) (3 x - 1)$
120 = 15x $^{1}$ - 5x
24 = 3x $^{1}$ - x
3x $^{1}$ - x - 24 = 0
3x $^{1}$ - 9x + 8x - 24 = 0
3x (x - 3) + 8(x - 3) = 0
(3x + 8)(x - 3) = 0
$x = 3, \frac{- 8}{3}$
Neglect the nagative value, x = 3
Thus, perpendicular = 15cm and base = 8cm
Now, from Pythagoras theorem,
H $^{1}$ = P $^{1}$ + B $^{1}$
H $^{1}$ = 15 $^{1}$ + 8 $^{1}$
H $^{1}$ = 225 + 64
H $^{1}$ = 289
H = 17cm

THE TRIANGLE AND ITS PROPERTIES

298389 Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion (A): If the altitudes from two vertices of a triangle to the opposite sides are equal, then the triangle is an isosceles triangle.
Reason (R): If two angles and one side of one triangle are equal to two angles and the corresponding side of the other triangle, then the two triangles are congruent.

1 Both A and R are true and R is the correct explanation of A.

2 Both A and R are true but R is not the correct explanation of A.

3 A is true but R is false.

4 A is false but R is true.

THE TRIANGLE AND ITS PROPERTIES

298390 By which of the following criterion two triangles cannot be proved congruent?

1 AAA.

2 SSS.

3 SAS.

4 ASA.

THE TRIANGLE AND ITS PROPERTIES

298391 Which is the longest side in the triangle PQR right angled at P?

1 PQ

2 QR

3 PR

4 None of these

THE TRIANGLE AND ITS PROPERTIES

298392 In a right-angled triangle, the angles other than the right angle are:

1 Obtuse.

2 Right.

3 Acute.

4 Straight.

Explanation:

Acute.
In right angled $△ ABC,$ $∠ B = 90^{\circ}$ [angle sum property of a triangle]
$∠ A + ∠ B + ∠ C = 180^{\circ}$
9
$\Rightarrow ∠ A + 90^{\circ} + ∠ C = 180^{\circ}$
$\Rightarrow ∠ A + ∠ C = 180^{\circ} - 90^{\circ} = 90^{\circ}$
Hence, in a right angled triangle, the angles other than the right angle are acute.

THE TRIANGLE AND ITS PROPERTIES

298387 The sides of a right triangle containing the right angle are (5x)cm and (3x-1)cm. If area of triangle be 60cm $^{1}$ , calculate the length of the sides of the triangle.

1 15cm, 8cm, 17cm

2 16cm, 8cm, 17cm

3 16cm, 8cm, 19cm

4 18cm, 8cm, 14cm

Explanation:

15cm, 8cm, 17cm
Given: In a right angled triangle, Perpendicular = 5x and Base = 3x - 1
Area = 60cm $^{1}$
Area of triangle $= \frac{1}{2}$ ?(base)(height)
$60 = \frac{1}{2} (5 x) (3 x - 1)$
120 = 15x $^{1}$ - 5x
24 = 3x $^{1}$ - x
3x $^{1}$ - x - 24 = 0
3x $^{1}$ - 9x + 8x - 24 = 0
3x (x - 3) + 8(x - 3) = 0
(3x + 8)(x - 3) = 0
$x = 3, \frac{- 8}{3}$
Neglect the nagative value, x = 3
Thus, perpendicular = 15cm and base = 8cm
Now, from Pythagoras theorem,
H $^{1}$ = P $^{1}$ + B $^{1}$
H $^{1}$ = 15 $^{1}$ + 8 $^{1}$
H $^{1}$ = 225 + 64
H $^{1}$ = 289
H = 17cm

THE TRIANGLE AND ITS PROPERTIES

298389 Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion (A): If the altitudes from two vertices of a triangle to the opposite sides are equal, then the triangle is an isosceles triangle.
Reason (R): If two angles and one side of one triangle are equal to two angles and the corresponding side of the other triangle, then the two triangles are congruent.

1 Both A and R are true and R is the correct explanation of A.

2 Both A and R are true but R is not the correct explanation of A.

3 A is true but R is false.

4 A is false but R is true.

THE TRIANGLE AND ITS PROPERTIES

298390 By which of the following criterion two triangles cannot be proved congruent?

1 AAA.

2 SSS.

3 SAS.

4 ASA.

THE TRIANGLE AND ITS PROPERTIES

298391 Which is the longest side in the triangle PQR right angled at P?

1 PQ

2 QR

3 PR

4 None of these

THE TRIANGLE AND ITS PROPERTIES

298392 In a right-angled triangle, the angles other than the right angle are:

1 Obtuse.

2 Right.

3 Acute.

4 Straight.

Explanation:

Acute.
In right angled $△ ABC,$ $∠ B = 90^{\circ}$ [angle sum property of a triangle]
$∠ A + ∠ B + ∠ C = 180^{\circ}$
9
$\Rightarrow ∠ A + 90^{\circ} + ∠ C = 180^{\circ}$
$\Rightarrow ∠ A + ∠ C = 180^{\circ} - 90^{\circ} = 90^{\circ}$
Hence, in a right angled triangle, the angles other than the right angle are acute.