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AREA PROBLEMS

Area Problems
The length of a rectangle is halved, while its breadth is tripled. What is the percentage change in area?

75% decrease
25% increase
50% increase
50% decrease

ANSWER EXPLANATION DOWNLOAD EXAMIANS APP

Let original length = x and original breadth = y. Original area = xy. New length = x . 2 New breadth = 3y. New area = ❨ x x 3y ❩ = 3 xy. 2 2 ∴ Increase % = ❨ 1 xy x 1 x 100 ❩% = 50%

Area Problems
A towel, when bleached, was found to have lost 20% of its length and 10% of its breadth. The percentage of decrease in area is:

20%
10.08%
10%
28%

ANSWER EXPLANATION DOWNLOAD EXAMIANS APP

Let original length = x and original breadth = y. Decrease in area = xy - ❨ 80 x x 90 y ❩ 100 100 = ❨ xy - 18 xy ❩ 25 = 7 xy. 25 ∴ Decrease % = ❨ 7 xy x 1 x 100 ❩% = 28%

Area Problems
The length of a rectangular plot is 20 metres more than its breadth. If the cost of fencing the plot @ 26.50 per metre is Rs. 5300, what is the length of the plot in metres?

Data inadequate
40
120
None of these

ANSWER EXPLANATION DOWNLOAD EXAMIANS APP

Let breadth = x metres. Then, length = (x + 20) metres. Perimeter = ❨ 5300 ❩ m = 200 m. 26.50 ∴ 2[(x + 20) + x] = 200 ⟹ 2x + 20 = 100 ⟹ 2x = 80 ⟹ x = 40. Hence, length = x + 20 = 60 m

Area Problems
The diagonal of the floor of a rectangular closet is 7½ feet. The shorter side of the closet is 4½ feet. What is the area of the closet in square feet?

27
5(1/4)
13(1/2)
37

ANSWER EXPLANATION DOWNLOAD EXAMIANS APP

Other side = (15 / 2) 2 - (9 / 2) 2 ft = (225 / 4) - (81 / 4) ft = 144 / 4 ft = 6 ft Area of closet = (6 x 4.5) sq. ft = 27 sq. ft.

Area Problems
A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 680 sq. feet, how many feet of fencing will be required?

40
88
34
68

ANSWER EXPLANATION DOWNLOAD EXAMIANS APP

We have: l = 20 ft and lb = 680 sq. ft. So, b = 34 ft. ∴ Length of fencing = (l + 2b) = (20 + 68) ft = 88 ft

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