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09. MENSURATION

290109 Mark $(✓)$ against the correct answer in the following:
The area of a rectangular carpet is 120m² and its perimeter is 46m. The length of its diagonal is:
Hint: l + b = 23 and lb = 120
Diagonal $= \sqrt{l^{2} + b^{2}} = \sqrt{289}$
$= \sqrt{17 \times 17} = 17$

1 15m

2 16m

3 17m

4 20m

Explanation:

17m
Area of rectangular carpet = 120cm²
Perimeter = 46m
Now 2(l + b)
= 46m
$\Rightarrow l + b = \frac{46}{2} = 23$
and lb = 120
$∴ (l - b)^{2} = (l + b)^{2} - 4 lb$
$= (23)^{2} - 4 \times 120$
$= 529 - 480$
$= 49 = (7)^{2}$
$∴ l - b = 7$
and l + b = 23
Adding we get, 2l = 30
$\Rightarrow l = \frac{30}{2}$
$= 15$
$∴$ b = 23 - 15 = 8
Now diagonal $= \sqrt{l^{2} + b^{2}}$
$= \sqrt{(15)^{2} + (8)^{2}}$
$= \sqrt{225 + 64}$
$= \sqrt{289}$
$= 17 m$

09. MENSURATION

290110 Mark $(✓)$ against the correct answer in the following:
The diameter of a circle is 7cm, its circumference is:

1 44cm

2 22cm

3 28cm

4 14cm

Explanation:

22cm
Circumference $= π d$
$= \frac{22}{7} \times 7$
$= 22 cm$ a

09. MENSURATION

290111 A rectangle ABCD, AC = 25 and CD = 7. Then, the perimeter of is:

1 62

2 75

3 89

4 100

Explanation:

62
AC = 25CD = 7CD = 7 By pythagoras theorem, AC $^{1}$ = AD $^{1}$ + DC $^{1}$ 625 = AD $^{1}$ + 49 AD $^{1}$ = 576 AD = 24 Hence, perimeter = 2 (7 + 24) = 62 units

09. MENSURATION

290112 Perimeter of a square whose side measures 4m is:

1 16m

2 16cm

3 4m

4 12m

09. MENSURATION

290109 Mark $(✓)$ against the correct answer in the following:
The area of a rectangular carpet is 120m² and its perimeter is 46m. The length of its diagonal is:
Hint: l + b = 23 and lb = 120
Diagonal $= \sqrt{l^{2} + b^{2}} = \sqrt{289}$
$= \sqrt{17 \times 17} = 17$

1 15m

2 16m

3 17m

4 20m

Explanation:

17m
Area of rectangular carpet = 120cm²
Perimeter = 46m
Now 2(l + b)
= 46m
$\Rightarrow l + b = \frac{46}{2} = 23$
and lb = 120
$∴ (l - b)^{2} = (l + b)^{2} - 4 lb$
$= (23)^{2} - 4 \times 120$
$= 529 - 480$
$= 49 = (7)^{2}$
$∴ l - b = 7$
and l + b = 23
Adding we get, 2l = 30
$\Rightarrow l = \frac{30}{2}$
$= 15$
$∴$ b = 23 - 15 = 8
Now diagonal $= \sqrt{l^{2} + b^{2}}$
$= \sqrt{(15)^{2} + (8)^{2}}$
$= \sqrt{225 + 64}$
$= \sqrt{289}$
$= 17 m$

09. MENSURATION

290110 Mark $(✓)$ against the correct answer in the following:
The diameter of a circle is 7cm, its circumference is:

1 44cm

2 22cm

3 28cm

4 14cm

Explanation:

22cm
Circumference $= π d$
$= \frac{22}{7} \times 7$
$= 22 cm$ a

09. MENSURATION

290111 A rectangle ABCD, AC = 25 and CD = 7. Then, the perimeter of is:

1 62

2 75

3 89

4 100

Explanation:

62
AC = 25CD = 7CD = 7 By pythagoras theorem, AC $^{1}$ = AD $^{1}$ + DC $^{1}$ 625 = AD $^{1}$ + 49 AD $^{1}$ = 576 AD = 24 Hence, perimeter = 2 (7 + 24) = 62 units

09. MENSURATION

290112 Perimeter of a square whose side measures 4m is:

1 16m

2 16cm

3 4m

4 12m

09. MENSURATION

290109 Mark $(✓)$ against the correct answer in the following:
The area of a rectangular carpet is 120m² and its perimeter is 46m. The length of its diagonal is:
Hint: l + b = 23 and lb = 120
Diagonal $= \sqrt{l^{2} + b^{2}} = \sqrt{289}$
$= \sqrt{17 \times 17} = 17$

1 15m

2 16m

3 17m

4 20m

Explanation:

17m
Area of rectangular carpet = 120cm²
Perimeter = 46m
Now 2(l + b)
= 46m
$\Rightarrow l + b = \frac{46}{2} = 23$
and lb = 120
$∴ (l - b)^{2} = (l + b)^{2} - 4 lb$
$= (23)^{2} - 4 \times 120$
$= 529 - 480$
$= 49 = (7)^{2}$
$∴ l - b = 7$
and l + b = 23
Adding we get, 2l = 30
$\Rightarrow l = \frac{30}{2}$
$= 15$
$∴$ b = 23 - 15 = 8
Now diagonal $= \sqrt{l^{2} + b^{2}}$
$= \sqrt{(15)^{2} + (8)^{2}}$
$= \sqrt{225 + 64}$
$= \sqrt{289}$
$= 17 m$

09. MENSURATION

290110 Mark $(✓)$ against the correct answer in the following:
The diameter of a circle is 7cm, its circumference is:

1 44cm

2 22cm

3 28cm

4 14cm

Explanation:

22cm
Circumference $= π d$
$= \frac{22}{7} \times 7$
$= 22 cm$ a

09. MENSURATION

290111 A rectangle ABCD, AC = 25 and CD = 7. Then, the perimeter of is:

1 62

2 75

3 89

4 100

Explanation:

62
AC = 25CD = 7CD = 7 By pythagoras theorem, AC $^{1}$ = AD $^{1}$ + DC $^{1}$ 625 = AD $^{1}$ + 49 AD $^{1}$ = 576 AD = 24 Hence, perimeter = 2 (7 + 24) = 62 units

09. MENSURATION

290112 Perimeter of a square whose side measures 4m is:

1 16m

2 16cm

3 4m

4 12m

09. MENSURATION

290109 Mark $(✓)$ against the correct answer in the following:
The area of a rectangular carpet is 120m² and its perimeter is 46m. The length of its diagonal is:
Hint: l + b = 23 and lb = 120
Diagonal $= \sqrt{l^{2} + b^{2}} = \sqrt{289}$
$= \sqrt{17 \times 17} = 17$

1 15m

2 16m

3 17m

4 20m

Explanation:

17m
Area of rectangular carpet = 120cm²
Perimeter = 46m
Now 2(l + b)
= 46m
$\Rightarrow l + b = \frac{46}{2} = 23$
and lb = 120
$∴ (l - b)^{2} = (l + b)^{2} - 4 lb$
$= (23)^{2} - 4 \times 120$
$= 529 - 480$
$= 49 = (7)^{2}$
$∴ l - b = 7$
and l + b = 23
Adding we get, 2l = 30
$\Rightarrow l = \frac{30}{2}$
$= 15$
$∴$ b = 23 - 15 = 8
Now diagonal $= \sqrt{l^{2} + b^{2}}$
$= \sqrt{(15)^{2} + (8)^{2}}$
$= \sqrt{225 + 64}$
$= \sqrt{289}$
$= 17 m$

09. MENSURATION

290110 Mark $(✓)$ against the correct answer in the following:
The diameter of a circle is 7cm, its circumference is:

1 44cm

2 22cm

3 28cm

4 14cm

Explanation:

22cm
Circumference $= π d$
$= \frac{22}{7} \times 7$
$= 22 cm$ a

09. MENSURATION

290111 A rectangle ABCD, AC = 25 and CD = 7. Then, the perimeter of is:

1 62

2 75

3 89

4 100

Explanation:

62
AC = 25CD = 7CD = 7 By pythagoras theorem, AC $^{1}$ = AD $^{1}$ + DC $^{1}$ 625 = AD $^{1}$ + 49 AD $^{1}$ = 576 AD = 24 Hence, perimeter = 2 (7 + 24) = 62 units

09. MENSURATION

290112 Perimeter of a square whose side measures 4m is:

1 16m

2 16cm

3 4m

4 12m