level – 1

1. The breadth of a rectangular park is two-thirds of its length. If the area of the park is 600 sq. m, then the difference between the length and breadth of the park is:
a) 6 m
b) 10 m
c) 12 m
d) 15 m

2. The length of a rectangular field is 4 times its breadth. A garden occupying 200 m² covers half of the total area of the field. What is the length of the field?
a) 20 m
b) 25 m
c) 40 m
d) 50 m

3. A rectangular lawn is 18 m long and 8 m wide. Find the length of the diagonal of a square lawn having the same area as the rectangular lawn.
a) 12√2
b) 6√6
c) 8√5
d) 10√3

4. A circular wire of diameter 28 cm is bent to form a rectangle whose sides are in the ratio 4 : 3. Find the area enclosed by the rectangle. (Take π = 22/7)
a) 336 cm²
b) 392 cm²
c) 448 cm²
d) 504 cm²

5. The difference between the length and breadth of a rectangle is 18 m. If its perimeter is 156 m, then the area of the rectangle is:
a) 1296 m²
b) 1404 m²
c) 1440 m²
d) 1512 m²

6. A rectangular pond of length 140 m and breadth 105 m is situated inside a circular park. If the area of the land portion of the park is 35,000 m², what is the radius of the park? (Take π = 22/7)
a) 105 m
b) 112 m
c) 119 m
d) 140 m

7. The length of a rectangular garden is 8 m more than its breadth. If the area of the garden is 384 m², then the length of the garden is:
a) 20 m
b) 24 m
c) 32 m
d) 40 m

8. The length and breadth of a rectangle are in the ratio 5 : 3. If its perimeter is 32 cm, then the area of the rectangle is:
a) 48 cm²
b) 60 cm²
c) 72 cm²
d) 96 cm²

9. The length and breadth of a rectangle are increased by 10% and 20% respectively. The percentage increase in the area of the rectangle is:
a) 30%
b) 32%
c) 35%
d) 40%

10. While measuring the sides of a rectangle, there is an excess of 10% in one side and a deficit of 5% in the other side. The percentage error in the calculated area is:
a) 5% increase
b) 4% increase
c) 5% decrease
d) 4% decrease

11. The area of a rectangle is twice the area of a square. The length of the rectangle is 18 cm and its breadth is 4/3 times the side of the square. The side of the square is:
a) 6 cm
b) 9 cm
c) 12 cm
d) 18 cm

12. Find the area of the largest circle that can be drawn inside a rectangle whose sides are 20 cm and 14 cm. (Take π = 22/7)
a) 154 cm²
b) 196 cm²
c) 220 cm²
d) 308 cm²

13. A goat is tied at the corner of a rectangular field measuring 25 m × 18 m with a rope of length 7 m. Find the area of the region that the goat can graze.
a) 38.5 m²
b) 49 m²
c) 77 m²
d) 154 m²

14. If the length of a rectangle is increased by 20% and its width is decreased by 25%, then the area of the rectangle will:
a) increase by 5%
b) decrease by 10%
c) remain unchanged
d) increase by 10%

15. The length of a rectangle is decreased by 20% and its breadth is increased by 10%. The percentage change in the area of the rectangle is:
a) 10% decrease
b) 12% decrease
c) 8% decrease
d) No change

16. If each side of a rectangle is increased by 10%, then the percentage increase in its area is:
a) 15%
b) 20%
c) 21%
d) 25%

17. The length of a rectangle is increased by 25%. By what percent should the breadth be decreased so that the area remains the same?
a) 15%
b) 20%
c) 25%
d) 30%

18. While measuring the sides of a rectangle, there is an excess of 20% in one side and a deficit of 20% in the other side. The percentage error in the calculated area is:
a) 4% increase
b) 4% decrease
c) No error
d) 8% decrease

19. If the length and breadth of a rectangle are each increased by 50%, then the percentage increase in its area is:
a) 100%
b) 125%
c) 150%
d) 200%

20. The perimeters of a rectangle and a circle are equal. If the area of the rectangle is A and the area of the circle is B, then which of the following is always true?
a) A > B
b) A = B
c) A < B
d) The relation between A and B cannot be determined

21. A rectangle is inscribed in a circle of diameter 13 cm. If one side of the rectangle is 5 cm, then the area of the rectangle is:
a) 30 cm²
b) 60 cm²
c) 48 cm²
d) 65 cm²

level – 2

1. The length and breadth of a rectangular park are in the ratio 5 : 3. If the perimeter of the park is 64 m, then the breadth of the park is:
a) 12 m
b) 18 m
c) 24 m
d) 30 m

2. The sides of a rectangular field are in the ratio 4 : 3 and its area is 432 sq. m. What is the perimeter of the field?
a) 72 m
b) 84 m
c) 96 m
d) 108 m

3. If the breadth and the perimeter of a rectangle are in the ratio 3 : 14, then the length and breadth of the rectangle are in the ratio:
a) 5 : 3
b) 4 : 3
c) 7 : 3
d) 5 : 2

4. If the length and the perimeter of a rectangle are in the ratio 4 : 14, then the length and breadth of the rectangle are in the ratio:
a) 3 : 2
b) 4 : 3
c) 5 : 3
d) 6 : 5

5. A circular wire of diameter 84 cm is cut and bent to form a rectangle whose sides are in the ratio 5 : 2. The smaller side of the rectangle is:
a) 12 cm
b) 14 cm
c) 20 cm
d) 28 cm

6. The length and breadth of a rectangular garden are in the ratio 7 : 3. If the perimeter of the garden is 80 m, find the breadth.
a) 10 m
b) 12 m
c) 14 m
d) 16 m

7. The sides of a rectangular field are in the ratio 5 : 4 and its area is 500 sq. m. Find the perimeter of the field.
a) 80 m
b) 85 m
c) 90 m
d) 95 m

8. The breadth and perimeter of a rectangle are in the ratio 1 : 5. Find the ratio of its length to breadth.
a) 2 : 1
b) 3 : 2
c) 4 : 1
d) 5 : 2

9. The length and perimeter of a rectangle are in the ratio 4 : 10. Find the ratio of its length to breadth.
a) 4 : 1
b) 3 : 2
c) 2 : 1
d) 5 : 2

10. A circular wire of diameter 49 cm is cut and reshaped into a rectangle whose sides are in the ratio 5 : 2. Find the smaller side of the rectangle. (π = 22/7)
a) 18 cm
b) 20 cm
c) 22 cm
d) 24 cm

level – 3

1. The floor of a hall is 80 m long and 5 m wide. Find the cost of covering the floor with a carpet 40 cm wide, at the rate of ₹20 per metre.
a) ₹8,000
b) ₹20,000
c) ₹12,000
d) ₹16,000

2. The cost of carpeting a rectangular room is ₹180. If the width had been 3 meters less, the cost of carpeting would have been ₹45 less. Find the width of the room.
a) 6 m
b) 9 m
c) 12 m
d) 15 m

3. A rectangular lawn 20 meters long and 12 meters broad is surrounded by a path of uniform width 2 meters. Find the cost of paving the path at ₹25 per square meters.
a) ₹5,600
b) ₹6,000
c) ₹6,400
d) ₹6,800

4. A rectangular hall is 60 m long and 4 m wide. Find the cost of covering the floor with a carpet 30 cm wide at the rate of ₹15 per metre.
a) ₹10,000
b) ₹11,000
c) ₹12,000
d) ₹13,000

5. The cost of carpeting a rectangular room is ₹240. If the width had been 4 metres less, the cost would have been ₹60 less. Find the width of the room.
a) 12 m
b) 14 m
c) 16 m
d) 18 m

6. A rectangular lawn 40 m long and 16 m wide is surrounded by a path of uniform width 2 m. Find the cost of paving the path at ₹25 per sq. m.
a) ₹5,400
b) ₹5,700
c) ₹6,000
d) ₹6,300

7. A rectangular corridor is 75 m long and 6 m wide. Find the cost of covering the floor with a carpet 50 cm wide at the rate of ₹18 per metre.
a) ₹14,200
b) ₹15,200
c) ₹16,200
d) ₹17,200

8. The cost of carpeting a rectangular room is ₹300. If the length had been 5 metres less, the cost would have been ₹75 less. Find the length of the room.
a) 16 m
b) 18 m
c) 20 m
d) 22 m

9. A rectangular lawn 30 m long and 20 m wide is surrounded by a path of uniform width 5 m. Find the cost of paving the path at ₹20 per sq. m.
a) ₹10,000
b) ₹11,000
c) ₹12,000
d) ₹13,000

10. The cost of carpeting a rectangular room is ₹360. If the length had been 6 metres less, the cost would have been ₹90 less. Find the length of the room.
a) 20 m
b) 22 m
c) 24 m
d) 26 m

ANSWERS