# Exercise : 3

1. What will be the ratio between the area of a rectangle and the area of a triangle with one of the sides of rectangle as base and a vertex on the opposite side of rectangle.
(a) 1 : 2
(b) 2 : 1
(c) 3 : 1
(e) None of these

#### View Ans & Explanation

Ans.b

Area of ΔEBC = 12 × BC × EF

= 12 × BC × AB[Since, EF = AB]

Area of ΔEBC = 12 × area of ΔABCD

\ Required ratio = 2 : 1.

2. Two roads XY and YZ of 15 metres and 20 metres length respectively are perpendicular to each other. What is the distance between X & Z by the shortest route?
(a) 35 metres
(b) 30 metres
(c) 24 metres
(d) 25 metres
(e) None of these

#### View Ans & Explanation

Ans.d

XYZ is a right-angled triangle

XZ = $\sqrt{15^{2} + 20^{2}} = \sqrt{625} = 25 \; m$

3. What will be the area of a semi-circle of 14 metres diameter?
(a) 154 sq metres
(b) 77 sq metres
(c) 308 sq metres
(d) 22 sq metres
(e) None of these

#### View Ans & Explanation

Ans.b

Area of semicircle = ½πr2

= ½ × 227 × 7 × 7 = 77 m2

4. The area of a right-angled triangle is two-thirds of the area of a rectangle. The base of the triangle is 80 percent of the breadth of the rectangle. If the perimeter of the rectangle is 200 cm, what is the height of the triangle?
(a) 20 cm
(b) 30 cm
(c) 15 cm
(e) None of these

#### View Ans & Explanation

Ans.d

Let the base and height of triangle, and length and breadth of rectangle be L and h, and L1 and b1 respectively.

Then 12 × L × h = 23 × L1 × b1 .....(i)

L = 45b1 .....(ii)

and L1 + b1 = 100 .....(iii)

In the above we have three equations and four unknowns. Hence the value of ‘h’ can’t be determined.

5. The area of a rectangular plot is 15 times its breadth. If the difference between the length and the breadth is 10 metres, what is its breadth?
(a) 10 metres
(b) 5 metres
(c) 7.5 metres
(e) None of these

#### View Ans & Explanation

Ans.b

L × B = 15 × B

∴ L = 15 m

and L – B = 10

∴ B = 15 – 10 = 5 m

6. A rectangular garden has a 5-metre-wide road outside around all the four sides. The area of the road is 600 square metres. What is the ratio between the length and the breadth of that plot?
(a) 3 : 2
(b) 4 : 3
(c) 5 : 4
(e) None of these

#### View Ans & Explanation

Ans.d

Area of shaded portion = 600 m.

∴ (l + 10)(b + 10) – lb = 600

or, lb + 10b + 10l + 100 – lb = 600

or, 10 (b + (l) = 500

∴ b + l = 50

From this equation we can’t get the required ratio.

7. Four sheets of 50 cm × 5 cm are to be arranged in such a manner that a square could be formed. What will be the area of inner part of the square so formed?
(a) 2000 cm2
(b) 1600 cm2
(c) 1800 cm2
(d) 2500 cm2
(e) None of these

#### View Ans & Explanation

Ans.e

The four sheets are BMRN, AMQL, NSKC and DLPK

∴ Side of the new square sheet = 50 + 5 = 55 cm and the side of the inner part of the square (55 – 10) = 45 cm

Hence, area = (45)2 = 2025 sq.cm.

8. In order to fence a square Manish fixed 48 poles. If the distance between two poles, is 5 metres then what will be the area of the square so formed?
(a) Cannot be determined
(b) 2600 cm2
(c) 2500 cm2
(d) 3025 cm2
(e) None of these

#### View Ans & Explanation

Ans.e

Let the side of the square be x m.

∴ Perimeter of the square = 48 × 5 = 4x ∴ x = 60 m

∴ Area = (60)2 = 3600 m2

9. The area of a side of a box is 120 sq cm. The area of the other side of the box is 72 sq cm. If the area of the upper surface of the box is 60 sq cm then find the volume of the box.
(a) 259200 cm3
(b) 86400 cm3
(c) 720 cm3
(d) Cannot be determined
(e) None of these

#### View Ans & Explanation

Ans.c

Volume of the box = $\sqrt{120 \times 72 \times 60}$ = 720 cm3

10. A circle and a rectangle have the same perimeter. The sides of the rectangle are 18 cm and 26 cm. What is the area of the circle ?
(a) 88 cm2
(b) 154 cm2
(c) 1250 cm2
(d) 616 cm2
(e) None of these

#### View Ans & Explanation

Ans.d

Perimeter of the circle = 2πr = 2(18 + 26)

⇒ 2 × 227 × r = 88 ⇒ r = 14

∴ Area of the circle

= πr2 = 227 × 14 × 14 = 616 cm2