Exercise : 4


1. The cost of carpeting a room 18 m long with a carpet 75 cm wide at 4.50 per metre is 810. The breadth of the room is:
(a) 7 m
(b) 7.5 m
(c) 8 m
(d) 8.5 m
(e) None of these
Ans.b

Length of the carpet = \(\frac{Total \; Cost}{Rate/m}\)

= (810045)m = 180 m.

Area of the room = Area of the carpet

= (180 × 75100) m2 = 135 m2

∴ Breadth of the room = \(\frac{Area}{Length} = \frac{135}{18} \; m\)

= 7.5 m

2. If the perimeter and diagonal of a rectangle are 14 and 5 cms respectively, find its area.
(a) 12 cm2
(b) 16 cm2
(c) 20 cm2
(d) 24 cm2
(e) None of these
Ans.a

In a rectangle,

\(\frac{\left(Perimeter \right)^{2}}{4} = \left(diagonal \right)^{2} + 2 \times area\)

\(\frac{\left(14 \right)^{2}}{4} = 5^{2} + 2 \times area\)

49 = 25 + 2 × area

∴ Area = \(\frac{49 - 25}{2} = \frac{24}{2} = 12 \; cm^{2}\)

3. In an isoscele right angled triangle, the perimeter is 20 metre. Find its area.
(a) 9,320 m2
(b) 8,750 m2
(c) 7,980 m2
(d) 6,890 m2
(e) None of these
Ans.a

In an isoscele right angled triangle,

Area = 23.3 × perimeter2

= 23.3 × 202 = 9320 m2

4. When the circumference and area of a circle are numerically equal, then the diameter is numerically equal to
(a) area
(b) circumference
(c) 4
(d) 2π
(e) None of these
Ans.c

According to question, circumference of circle = Area of circle

or πd = π(d2)2 [where d = diameter]

∴ d = 4

5. In a parallelogram, the length of one diagonal and the perpendicular dropped on that diagonal are 30 and 20 metres respectively. Find its area.
(a) 600 m2
(b) 540 m2
(c) 680 m2
(d) 574 m2
(e) None of these
Ans.a

In a parallelogram.

Area = Diagonal × length of perpendicular on it.

= 30 × 20 = 600 m2

6. The diameter of a garden roller is 1.4 m and it is 2 m long. How much area will it cover in 5 revolutions ? (use π = 227)
(a) 40 m2
(b) 44 m2
(c) 48 m2
(d) 36 m2
(e) None of these
Ans.b

Required area covered in 5 revolutions

= 5 × 2πrh = 5 × 2 × 227 × 0.7 × 2 = 44 m2

7. The area of a triangle is 615 m2. If one of its sides is 123 metre, find the length of the perpendicular dropped on that side from opposite vertex.
(a) 15 metres
(b) 12 metres
(c) 10 metres
(d) 9 metres
(e) None of these
Ans.c

In a triangle,

Area = 12 × length of perpendicular × base

or 615 = 12 × length of perpendicular × 123

∴ Length of perpendicular = \(\frac{615 \times 2}{123} = 10 \; m\)

8. A horse is tethered to one corner of a rectangular grassy field 40 m by 24 m with a rope 14 m long. Over how much area of the field can it graze?
(a) 154 cm2
(b) 308 m2
(c) 150 m2
(d) 407 m2
(e) None of these
Ans.a

quant

Area of the shaded portion

= 14 × π × (14)2 = 154 m2

9. How many plants will be there in a circular bed whose outer edge measure 30 cms, allowing 4 cm2 for each plant ?
(a) 18
(b) 750
(c) 24
(d) 120
(e) None of these
Ans.a

Circumference of circular bed = 30 cm

Area of circular bed = (30)2

Space for each plant = 4 cm2

∴ Required number of plants

= (30)2 ÷ 4 = 17.89 = 18(approx)

10. From a square piece of a paper having each side equal to 10 cm, the largest possible circle is being cut out. The ratio of the area of the circle to the area of the original square is nearly :
(a) 45
(b) 35
(c) 56
(d) 67
(e) None of these
Ans.a

Area of the square = (10)2 = 100 cm2

The largest possible circle would be as shown in the figure below :

quant

Area of the circle = 227 × (5)2 = \(\frac{22 \times 25}{7}\)

Required ratio = \(\frac{22 \times 25}{7 \times 100} = \frac{22}{28} = \frac{11}{14}\)

= 0.785 ≈ 0.8 = 45