This set of Aptitude Questions and Answers (MCQs) focuses on “Rectangles and Squares – Set 2”.
1. What will be the area of the square if one of its diagonals is 7 m long?
a) 49 m2
b) 49 cm2
c) 24.5 m2
d) 343 cm2
View Answer
Explanation: Given,
d = 7m
Area of square = \(\frac {1}{2}\) (d)2
= \(\frac {1}{2}\) * 72
= 24.5 m2
2. What will be the percentage increase in the area of the square if each of its side is increased by 10%?
a) 21%
b) 42%
c) 36%
d) 10.5%
View Answer
Explanation: Let the original length of the side of square be a units.
➩ Original area = a2
➩ New length = a + ((10 / 100) a)
➩ a + 0.1 a
➩ 1.1 a
➩ New area = (1.1 a)2
➩ 1.21 a2
➩ % increase = ((new area – original area) / original area) * 100
➩ ((1.21a2 – a2) / a2) * 100
➩ (0.21a2 / a2) * 100
➩ 21%
3. If the area of a rectangle is 990m2. If the length is 10% more than the breadth, then what will be the breadth of the rectangular field?
a) 60
b) 30
c) 33
d) 66
View Answer
Explanation: Let the breadth = x m.
➩ Then length = (110x / 100) m
➩ x * (110x / 100) = 990
➩ x2 = 990 * 100 / 110
➩ x2 = 900
➩ x = 30m
4. A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 600 sq. ft, then how many feet of fencing will be required?
a) 80
b) 88
c) 70
d) 90
View Answer
Explanation: Given,
Area of rectangle = 600
➩ 20 * breadth = 600
➩ Breadth = 30 feet
Length to be fenced = 2 * breadth + length
➩ Length to be fenced = 2 * 30 + 20
= 60 + 20
= 80 feet
5. The perimeters of two squares are 40 cm and 32 cm. What will be the perimeter of a third square whose area is equal to the difference of the areas of the two squares?
a) 76 cm
b) 84 cm
c) 96 cm
d) 52 cm
View Answer
Explanation: Given,
First square:
L1 = 40 cm
Area = L12 = 402 = 1600 cm2
Second square:
L2 = 32 cm
Area = L22 = 322 = 1024 cm2.
Difference of area = 1600 cm2 – 1024 cm2 = 576 cm2
Area of new square = 576 cm2. Let its side length be L3.
➩ L32 = 576 cm2
➩ L3 = 24 cm.
Thus, perimeter of new square = 4 * L3 = 4 * 24 = 96 cm.
6. What will be the ratio of the area of two squares which have their diagonals in the ratio 3:5?
a) 16:25
b) 3:5
c) 2:5
d) 9:25
View Answer
Explanation: Let the diagonals be 3y and 5y.
Area of the square = (1 / 2) * diagonal2
Thus,
➩ (1 / 2) * (3y)2 : (1 / 2) * (5y)2
➩ 9y2 : 25y2
➩ 9:25
7. A courtyard is 25 meter long and 20 meter broad is to be paved with bricks of dimensions 20 cm by 10 cm. What will be the number of bricks required?
a) 25000
b) 20000
c) 27000
d) 30000
View Answer
Explanation: Number of bricks = Area of courtyard / area of 1 brick
➩ Number of bricks = (2500 * 2000) / (20 * 10)
➩ Number of bricks = 5000000 / 200
➩ Number of bricks = 25000
8. 50 square stone slabs of equal size were needed to cover a floor area of 800 sq. m. What will be the length of each stone slab?
a) 520 cm
b) 500 cm
c) 400 cm
d) 425 cm
View Answer
Explanation: Area of each slab = Floor area / number of slabs
= 800 / 50
= 16 sq. m
Length of each slab = (16)1/2
= 4 m = 400 cm
9. A towel, when bleached, was found to have lost 25% of its length and 10% of its breadth. What will be the percentage decrease in the area?
a) 35.6%
b) 32.5%
c) 30.2%
d) 25.8%
View Answer
Explanation: Let original length = x and breadth = y.
Original area = xy
New length = 75x / 100 and breadth = 90y / 100
New area = 75x / 100 * 90y / 100
= 0.675 xy
Decrease in area = Original area – New area
= xy – 0.675 xy
= 0.325 xy
%decrease = 0.325xy / xy * 100
= 32.5%
10. The length of a room is 6 m and width are 4 m. What will be the cost (in Rs.) of paving the floor by slabs at the rate of Rs.700 per sq meter?
a) 16800
b) 14400
c) 12800
d) 15700
View Answer
Explanation: Area of room = l * b
= 6 * 4
= 24 sq. m
Cost of paving = rate of paving * area
= Rs.700 per sq. m * 24 sq. m
= Rs 16800
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