Area problems
- 1. Angles of a quadrilateral are in the ratio 3 : 4 : 5 : 8. The smallest angle is
Options- A. 54°
- B. 40°
- C. 36°
- D. 18° Discuss
Correct Answer: 54°
Explanation:
Let First angle = 3k
Second angle = 4k
Third angle = 5k and
Fourth angle = 8k
We know 3k + 4k + 5k + 8k = 360°
? 20k = 360°
? k = 18 °
Measure of smallest angle = 3k
=3 x 18 °
= 54 °
- 2. Floor of a square room of side 10 m is to be completely covered with square tiles, each having length 50 cm. The smallest number of tiles needed is?
Options- A. 200
- B. 300
- C. 400
- D. 500 Discuss
Correct Answer: 400
Explanation:
Area of square room = (10)2 = 100 sq m
= 100 x (100)2 sq cm
= 100 x 100 x 100 sq cm
Now, area of tiles = (50)2 = 50 x 50 sq cm
? Number of tiles needed = (Area of square room) / (Area of tile)
= (100 x 100 x 100) / (50 x 50)
= 400
Hence, 400 tiles will be needed.
- 3. The perimeter of an isosceles triangle is 26 cm while equal sides together measure 20 cm. The third side and each of the equal sides are respectively.
Options- A. 6 cm and 10 cm
- B. 8 cm and 9 cm
- C. 10 cm and 8 cm
- D. 14 cm and 6 cm Discuss
Correct Answer: 6 cm and 10 cm
Explanation:
Let the third side be x.
According to the question,
x + 20 = 26
? x = 26 - 20 = 6 cm
? Each equal side = 20/2 = 10 cm
- 4. The ratio of length and breadth of a rectangle is 5 : 3 .If length is 8 m more than breadth, find the area of the rectangle.
Options- A. 300 sq m
- B. 250 sq m
- C. 240 sq m
- D. 185 sq m Discuss
Correct Answer: 240 sq m
Explanation:
Let length of rectangle = 5k
and breadth of rectangle = 3k
According to the quecation,
5k - 3k = 8
? 2k =8
? k = 4
? Lenght = 5k = 5 x 4 = 20 m
Breadth = 3k = 3 x 4 = 12 m
? Required area = Lenght x Breadth
= 20 x 12 = 240 sq m
- 5. The ratio between the lenght and the breadth of a rectangle is 2 : 1. If breadth is 5 cm less than the length, what will be the parimeter of the rectangle?
Options- A. 30 cm
- B. 25 cm
- C. 35 cm
- D. 40 cm Discuss
Correct Answer: 30 cm
Explanation:
Let length = 2x and breadth = x
According to the question,
2x - x = 5
? x = 5
? Required perimeter = 2(2x + x)
= 6x
= 30 cm
- 6. The perimeter of a rectangle having area equal to 144 cm 2 and sides in the ratio 4 : 9 is
Options- A. 52 cm
- B. 56 cm
- C. 60 cm
- D. 64 cm Discuss
Correct Answer: 52 cm
Explanation:
Let l = 4k and b = 9k
Area of rectangle = l x b
144 = 4k x 9k
? k2 = 144/36
? k2 = 4
? k = 2
? l = 8 cm and b = 18 cm
Perimeter of rectangle = 2(l + b)
= 2(8 + 18)
= 2 x 26
= 52 cm
- 7. Area of rectangular field is 3584 m 2 and the length and the breadth are in the ratio 7 : 2, respectively. What is the perimeter of the rectangle?
Options- A. 246 m
- B. 292 m
- C. 286 m
- D. 288 m Discuss
Correct Answer: 288 m
Explanation:
Let length of the rectangular field = 7k m
and breadth of the rectangular field = 2k m
According to the question,
Area of a rectangular field = Length x Breadth
? 3584 = 7k x 2k
? 14 x k2 = 3584
? k2 = 3584/14 = 256
? k2 = 256 = 16 m
? Length of rectangular field = 7k = 7 x 16 = 112 m
And breadth of rectangular field = 2 x 16 = 32 m
? Perimeter of rectangle = 2(Length x Breadth)
= 2(112 + 32)
= 2 x 144
= 288 m
- 8. The length and perimeter of a rectangle are the ratio of 5 : 18 What well be the ratio of its length and breadth?
Options- A. 4 : 3
- B. 3 : 5
- C. 5 : 4
- D. 4 : 7 Discuss
Correct Answer: 5 : 4
Explanation:
According to the question,
l/[2(l + b)] = 5/18
? 10l + 10b = 18l = 10b
? l/b = 10/8 = 5/4
? l : b = 5 : 4
Hence, ratio of length and breadth of a rectangle is 5 : 4
- 9. Find the cost of carpeting a room 8 m long and 6 m broad with a carpet 75 cm wide at ? 20 per m.
Options- A. ? 1300
- B. ? 1500
- C. ? 1750
- D. ? 1280 Discuss
Correct Answer: ? 1280
Explanation:
Area of the carpet = Area of the room
= 8 x 6 = 48 sq m
Width of the carpet = 75/100 = 3/4 m
Length of the carpet = 48 x (4/3)
= 16 x 4 = 64 m
? Cost of carpeting = 64 x 20 = ? 1280
- 10. A rectangle has 20 cm as its length and 200 sq cm as its area. If the area is increased by 1 1/ 5 time the original area by increase its length only then the perimeter of the rectangle so formed (in cm) is
Options- A. 72
- B. 60
- C. 64
- D. 68 Discuss
Correct Answer: 68
Explanation:
l1 = 20 cm, A1 = 200 sq cm
? b1 = 200/20 = 10 cm
Now, A2 = 200 x 6/5 = 240 sq cm
b2 = 10 cm
? l2 = 240/10 = 24 cm
? Perimeter of new rectangle = 2(l2 + b2)
= 2(24 + 10) = 2 x 34 = 68 cm
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