Question

If the length of a certain rectangle is decreased by 4cm and the width is increased by 3cm,a square with the same area would result.find the perimeter of original rectangle

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Answer 1

The perimeter is 50

Explanation:

The original area is LW

The new area is (L-4)(W+3)

These areas are the same

1: (L-4)(W+3)=LW

You are also told that the new figure is a square, hence

2: (L-4)=(W+3)

Equation (2) implies

3: L=W+7

Substitute for L in Equation (1) and solve for W

(W+7-4)(W+3)=(W+7)W

W^2+3W+7W+21-4W-12=W^2+7W

6W+9=7W

W=9

Now use Equation (3) to solve for L

L=16

The perimeter is 2W+2L

P=18+32=50