298311
The hypotenuse of a right triangle is 26cm long. If one of the remaining two sides is 10cm long, the length of the other side is:
1 25cm
2 23cm
3 24cm
4 22cm
Explanation:
24cm 2 In right traingle BOC, BC\(^{1}\) = OC\(^{1}\) + OB\(^{1}\) (26)\(^{1}\) = (10)\(^{1}\) + OB\(^{1}\) 676 =\(^{1}\)100 + OB\(^{1}\) OB\(^{1}\) = 576 OB\(^{1}\) = (24)\(^{1}\) OB = 24cm Hence, the correct answer is option (c).
THE TRIANGLE AND ITS PROPERTIES
298312
Find the value of x in given figure. 3
1 120°
2 50°
3 60°
4 180°
Explanation:
60° The exterior angle (120°) is equal to the sum of the two opposite interior angles (60° + x) Thus, 120° = 60° + x x = 60°
THE TRIANGLE AND ITS PROPERTIES
298313
In which of the following cases can a right triangle ABC be constructed?
1 AB = 5cm, BC = 7cm, AC = 10cm
2 AB = 7cm, BC = 8cm, AC = 12cm
3 AB = 8cm, BC = 17cm, AC = 15cm
4 None of these.
Explanation:
AB = 8cm, BC = 17cm, AC = 15cm In (c) BC\(^{1}\) = AC\(^{1}\) + AB\(^{1}\) (17)\(^{1}\) = (15)\(^{1}\) + (8)\(^{1}\) 289 =\(^{1}\)225 + 64 289 = 289 Since, the sum of the square of two smallest side is equal to the square of largest side. Hence, ABC is a right angle triangle at A. Hence, the correct answer is option (c).
THE TRIANGLE AND ITS PROPERTIES
298314
The top of a broken tree touches the ground at a distance of 12m from its base. If the tree is broken at a height of 5m from the ground then the actual height of the tree is:
1 25m
2 13m
3 18m
4 17m
Explanation:
18m Let AB be the given that tree of height h m, which is broken at D which is 12m away from its base and the height of remaining part, i.e. CS is 5m. 4 Now, Ab = AC = BC AC = AB - BC = h - 5 AC = CD = h - 5 ...(i) In right angled \(\triangle\text{BDC},\) CD\(^{1}\) = CB\(^{1}\) + BD\(^{1}\) [by pythagoras theoram] (h - 5)\(^{1}\) = (5)\(^{1}\) + (12)\(^{1}\) [from Eq. (i)] (h - 5)\(^{1}\) = 25 + 144 (h - 5)\(^{1}\) = 169 \(?\text{ h} - 5 =\sqrt{169}=13\) \(? \text{h} = 13 + 5\) \(? \text{h} = 18\text{m}\) Hence, the height of the tree is 18m.
298311
The hypotenuse of a right triangle is 26cm long. If one of the remaining two sides is 10cm long, the length of the other side is:
1 25cm
2 23cm
3 24cm
4 22cm
Explanation:
24cm 2 In right traingle BOC, BC\(^{1}\) = OC\(^{1}\) + OB\(^{1}\) (26)\(^{1}\) = (10)\(^{1}\) + OB\(^{1}\) 676 =\(^{1}\)100 + OB\(^{1}\) OB\(^{1}\) = 576 OB\(^{1}\) = (24)\(^{1}\) OB = 24cm Hence, the correct answer is option (c).
THE TRIANGLE AND ITS PROPERTIES
298312
Find the value of x in given figure. 3
1 120°
2 50°
3 60°
4 180°
Explanation:
60° The exterior angle (120°) is equal to the sum of the two opposite interior angles (60° + x) Thus, 120° = 60° + x x = 60°
THE TRIANGLE AND ITS PROPERTIES
298313
In which of the following cases can a right triangle ABC be constructed?
1 AB = 5cm, BC = 7cm, AC = 10cm
2 AB = 7cm, BC = 8cm, AC = 12cm
3 AB = 8cm, BC = 17cm, AC = 15cm
4 None of these.
Explanation:
AB = 8cm, BC = 17cm, AC = 15cm In (c) BC\(^{1}\) = AC\(^{1}\) + AB\(^{1}\) (17)\(^{1}\) = (15)\(^{1}\) + (8)\(^{1}\) 289 =\(^{1}\)225 + 64 289 = 289 Since, the sum of the square of two smallest side is equal to the square of largest side. Hence, ABC is a right angle triangle at A. Hence, the correct answer is option (c).
THE TRIANGLE AND ITS PROPERTIES
298314
The top of a broken tree touches the ground at a distance of 12m from its base. If the tree is broken at a height of 5m from the ground then the actual height of the tree is:
1 25m
2 13m
3 18m
4 17m
Explanation:
18m Let AB be the given that tree of height h m, which is broken at D which is 12m away from its base and the height of remaining part, i.e. CS is 5m. 4 Now, Ab = AC = BC AC = AB - BC = h - 5 AC = CD = h - 5 ...(i) In right angled \(\triangle\text{BDC},\) CD\(^{1}\) = CB\(^{1}\) + BD\(^{1}\) [by pythagoras theoram] (h - 5)\(^{1}\) = (5)\(^{1}\) + (12)\(^{1}\) [from Eq. (i)] (h - 5)\(^{1}\) = 25 + 144 (h - 5)\(^{1}\) = 169 \(?\text{ h} - 5 =\sqrt{169}=13\) \(? \text{h} = 13 + 5\) \(? \text{h} = 18\text{m}\) Hence, the height of the tree is 18m.
298311
The hypotenuse of a right triangle is 26cm long. If one of the remaining two sides is 10cm long, the length of the other side is:
1 25cm
2 23cm
3 24cm
4 22cm
Explanation:
24cm 2 In right traingle BOC, BC\(^{1}\) = OC\(^{1}\) + OB\(^{1}\) (26)\(^{1}\) = (10)\(^{1}\) + OB\(^{1}\) 676 =\(^{1}\)100 + OB\(^{1}\) OB\(^{1}\) = 576 OB\(^{1}\) = (24)\(^{1}\) OB = 24cm Hence, the correct answer is option (c).
THE TRIANGLE AND ITS PROPERTIES
298312
Find the value of x in given figure. 3
1 120°
2 50°
3 60°
4 180°
Explanation:
60° The exterior angle (120°) is equal to the sum of the two opposite interior angles (60° + x) Thus, 120° = 60° + x x = 60°
THE TRIANGLE AND ITS PROPERTIES
298313
In which of the following cases can a right triangle ABC be constructed?
1 AB = 5cm, BC = 7cm, AC = 10cm
2 AB = 7cm, BC = 8cm, AC = 12cm
3 AB = 8cm, BC = 17cm, AC = 15cm
4 None of these.
Explanation:
AB = 8cm, BC = 17cm, AC = 15cm In (c) BC\(^{1}\) = AC\(^{1}\) + AB\(^{1}\) (17)\(^{1}\) = (15)\(^{1}\) + (8)\(^{1}\) 289 =\(^{1}\)225 + 64 289 = 289 Since, the sum of the square of two smallest side is equal to the square of largest side. Hence, ABC is a right angle triangle at A. Hence, the correct answer is option (c).
THE TRIANGLE AND ITS PROPERTIES
298314
The top of a broken tree touches the ground at a distance of 12m from its base. If the tree is broken at a height of 5m from the ground then the actual height of the tree is:
1 25m
2 13m
3 18m
4 17m
Explanation:
18m Let AB be the given that tree of height h m, which is broken at D which is 12m away from its base and the height of remaining part, i.e. CS is 5m. 4 Now, Ab = AC = BC AC = AB - BC = h - 5 AC = CD = h - 5 ...(i) In right angled \(\triangle\text{BDC},\) CD\(^{1}\) = CB\(^{1}\) + BD\(^{1}\) [by pythagoras theoram] (h - 5)\(^{1}\) = (5)\(^{1}\) + (12)\(^{1}\) [from Eq. (i)] (h - 5)\(^{1}\) = 25 + 144 (h - 5)\(^{1}\) = 169 \(?\text{ h} - 5 =\sqrt{169}=13\) \(? \text{h} = 13 + 5\) \(? \text{h} = 18\text{m}\) Hence, the height of the tree is 18m.
298311
The hypotenuse of a right triangle is 26cm long. If one of the remaining two sides is 10cm long, the length of the other side is:
1 25cm
2 23cm
3 24cm
4 22cm
Explanation:
24cm 2 In right traingle BOC, BC\(^{1}\) = OC\(^{1}\) + OB\(^{1}\) (26)\(^{1}\) = (10)\(^{1}\) + OB\(^{1}\) 676 =\(^{1}\)100 + OB\(^{1}\) OB\(^{1}\) = 576 OB\(^{1}\) = (24)\(^{1}\) OB = 24cm Hence, the correct answer is option (c).
THE TRIANGLE AND ITS PROPERTIES
298312
Find the value of x in given figure. 3
1 120°
2 50°
3 60°
4 180°
Explanation:
60° The exterior angle (120°) is equal to the sum of the two opposite interior angles (60° + x) Thus, 120° = 60° + x x = 60°
THE TRIANGLE AND ITS PROPERTIES
298313
In which of the following cases can a right triangle ABC be constructed?
1 AB = 5cm, BC = 7cm, AC = 10cm
2 AB = 7cm, BC = 8cm, AC = 12cm
3 AB = 8cm, BC = 17cm, AC = 15cm
4 None of these.
Explanation:
AB = 8cm, BC = 17cm, AC = 15cm In (c) BC\(^{1}\) = AC\(^{1}\) + AB\(^{1}\) (17)\(^{1}\) = (15)\(^{1}\) + (8)\(^{1}\) 289 =\(^{1}\)225 + 64 289 = 289 Since, the sum of the square of two smallest side is equal to the square of largest side. Hence, ABC is a right angle triangle at A. Hence, the correct answer is option (c).
THE TRIANGLE AND ITS PROPERTIES
298314
The top of a broken tree touches the ground at a distance of 12m from its base. If the tree is broken at a height of 5m from the ground then the actual height of the tree is:
1 25m
2 13m
3 18m
4 17m
Explanation:
18m Let AB be the given that tree of height h m, which is broken at D which is 12m away from its base and the height of remaining part, i.e. CS is 5m. 4 Now, Ab = AC = BC AC = AB - BC = h - 5 AC = CD = h - 5 ...(i) In right angled \(\triangle\text{BDC},\) CD\(^{1}\) = CB\(^{1}\) + BD\(^{1}\) [by pythagoras theoram] (h - 5)\(^{1}\) = (5)\(^{1}\) + (12)\(^{1}\) [from Eq. (i)] (h - 5)\(^{1}\) = 25 + 144 (h - 5)\(^{1}\) = 169 \(?\text{ h} - 5 =\sqrt{169}=13\) \(? \text{h} = 13 + 5\) \(? \text{h} = 18\text{m}\) Hence, the height of the tree is 18m.
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