Area problems
- 1. If the sides of a rectangle are increased by 10% find the percentage increased in its diagonals.
Options- A. 20%
- B. 10%
- C. 15%
- D. 18% Discuss
Correct Answer: 10%
Explanation:
According to the formula,
? Percentage increase in sides = 10%
? Percentage increase diagonals = 10%
- 2. What is the diameter of the circle having 3 cm radius?
Options- A. 6 cm
- B. 12 cm
- C. 1.5 cm
- D. 8 cm Discuss
Correct Answer: 6 cm
Explanation:
Radius = Diameter/2
? Diameter = 2 x Radius
= 2 x 3
= 6 cm
- 3. The radius of a circular field is 25 m. Find the area of the field.
Options- A. 125 ? sq m
- B. 625 ? sq m
- C. 25 ? sq m
- D. 135 ? sq m Discuss
Correct Answer: 625 ? sq m
Explanation:
Required area = ?r2 = ? x 25 x 25
= 625? sq m.
- 4. The length and breadth of a rectangular piece of land are in the ratio of 5:3, the owner spent Rs.3000 for surrounding it from all the sides at Rs.7.50 per meter. The different between its length and breadth is?
Options- A. 50 m
- B. 100 m
- C. 150 m
- D. 200 m Discuss
Correct Answer: 50 m
Explanation:
Let Length = 5y meters and breadth = 3y meters.
Then, perimeter = 2 x (5y + 3y ) m = 16y meters ...(i)
But perimeter = Total Cost / Rate = 3000 / 7.50 m = 400 m ...(ii)
from eqs. (i) and (ii)
16y = 400
? y = 25
? Length - Breadth = (5 x 25 - 3 x 25 ) m
= 2 x 25 m
= 50 m
- 5. One side of a rectangular field is 4 meter and its diagonal is 5 meter. The area of the field is?
Options- A. 12 m2
- B. 15 m2
- C. 20 m 2
- D. 4?5 m2 Discuss
Correct Answer: 12 m2
Explanation:
Other side = ?5 2 - 42
= ? 9
=3 m
So The area of the rectangular field = 4 x 3
= 12 m2
- 6. If the base of a rectangular is increased by 10% and the area is unchanged , then the corresponding altitude must to be decreased by?
Options- A. 91/11 %
- B. 10%
- C. 11%
- D. 111/9 % Discuss
Correct Answer: 91/11 %
Explanation:
Let base = b and altitude = h
Then, Area = b x h
But New base = 110b / 100 = 11b / 10
Let New altitude = H
Then,
Decrese = (h - 10h /11 )
= h / 11
? Required decrease per cent
= (h/11) x (1 / h ) x 100 %
= 91/11 %
- 7. The length of hall is (4/3) times its breadth. If the area of hall be 300 square meters, the difference between the length and the breadth is?
Options- A. 15 meters
- B. 4 meters
- C. 3 meters
- D. None of these Discuss
Correct Answer: None of these
Explanation:
Let breadth = b meters.
Then, length = 4b/3 meters.
? b x 4b/3 = 300
? b2 = 300 x 3/4
? b2 = 225
? b = 15
Hence, required difference = [(Length) - (Breadth) ]
= 4b/3 - b
= b/3
= 15/3 m
= 5 m
- 8. The cost of cultivating a square field at the rate of Rs. 160 per hectare is Rs. 1440. the cost of putting a fence around it at 75 paisa per meter is?
Options- A. Rs. 900
- B. Rs. 1800
- C. Rs. 360
- D. Rs. 810 Discuss
Correct Answer: Rs. 900
Explanation:
Area = 1440 / 160 hectares
= 9 hectares
= 90000 m2
? One side = ?90000 m
= 300 m
So perimeter = 4 x 300 m
= 1200 m
? Cost of fencing = Rs (1200 x 75) / 100
= Rs. 900
- 9. A rectangular plot is half as long again as it broad. The area of the lawn is 2/3 hectares. The length of the plot is?
Options- A. 100 meters
- B. 66.66 meters
- C. 33 meters
- D. (100/ ? 3 ) meters Discuss
Correct Answer: 100 meters
Explanation:
Let breadth = b meters.
then, length = 3b/2 meters
? b x 3b/2 = 2/3 X 10000
? b2 = (4 x 10000)/9
? b = ( 2 X 100)/3 m
? Length = (3/2) x (2/3) x 100 m
= 100 m
- 10. The ratio between the length and breadth of a rectangular field is 5:4. If the breadth is 20 meters less than the length, the perimeters of the field is?
Options- A. 260 m
- B. 280 m
- C. 360 m
- D. none of these Discuss
Correct Answer: 360 m
Explanation:
Let length of rectangular field = 5y,
so width = 4y.
From question
5y - 4y = 20m
? x = 20m
? Length = (5 x 20)m = 100 m
Breadth = (4 x 20) m = 80 m
? Perimeter = 2 (100 + 80 ) m = 360 m
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