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Question

The perimeter of the bigger rectangle is 430 ft and smaller rectangle is x - 3y = 30. As per the given information, the area of bigger rectangle is .

A
3,562 ft2
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B
3,016 ft2
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C
8,016 ft2
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D
8,816 ft2
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Solution

The correct option is C 8,016 ft2
Given, perimeter of a bigger rectangle is 430 ft.
Perimeter of a rectangle = 2(l + b)
2((3x + 5) + 6y) = 430
6x + 10 + 12y = 430
6x + 12y = 430 - 10
6x + 12y = 420 ----------(1)
Perimeter of smaller rectangle is
given as
x - 3y = 30-------------(2)

Multiply equation (2) with 4 we get:
4x - 12y = 120-------------(3)

Adding equations (2) and (3)
6x + 12y + 4x - 12y = 420 + 120
10x = 420 + 120
10x = 540
x = 54010
x = 54

Substitute x value in equation (1)
6(54) + 12y = 420
324 + 12y = 420
12y = 420 - 324
12y = 96
y = 8

Area = Length × Width
= (3x + 5) × 6y
= [3(54) + 5] × 6(8)
= (162 + 5) × 48
= 167 × 48
= 8,016 ft2

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