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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 ft2Given, 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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