The length of a rectangular lot is 7 yards less than twice its width. If the length was increased by 11 yards and the width decreased by 6 yards, the area would be decreased by 40 square yards. Find the original dimension of the lot.

Question

Deborah Walker

Mathematics

25 November, 08:04

The length of a rectangular lot is 7 yards less than twice its width. If the length was increased by 11 yards and the width decreased by 6 yards, the area would be decreased by 40 square yards. Find the original dimension of the lot.

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Answers (1)

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Raegan · Answer 1

The width = 16 yards and the length = 25 yards.

Step-by-step explanation:

Let x yards be the original width, then the original length is 2x - 7 yards.

Therefore the original area = x (2x - 7) yd^2.

The new area = (2x - 7 + 11) (x - 6)

= (2x + 4) (x - 6) yd^2.

So we have the equation

x (2x - 7) - (2x + 4) (x - 6) = 40

2x^2 - 7x - (2x^2 - 12x + 4x - 24) = 40

2x^2 - 7x - 2x^2 + 8x + 24 - 40 = 0

x - 16 = 0

x = 16 yards = the width.

The length = 2 (16) - 7 = 25 yards.