1. If the length of a rectangle is decreased by 4 cm and the width is increased by 5 cm, the result will be a square, the area of which will be 40 cm2 greater than the area of the rectangle. Find the area of the rectangle.

2. The perimeter of a rectangle is 30 cm. If its length is decreased by 3 cm and its width is increased by 5 cm, the area of the rectangle will decrease by 8 cm2. Find the area of the original rectangle.

Question

Mathematics

Cristopher Boyer

12 May, 21:32

1. If the length of a rectangle is decreased by 4 cm and the width is increased by 5 cm, the result will be a square, the area of which will be 40 cm2 greater than the area of the rectangle. Find the area of the rectangle.

2. The perimeter of a rectangle is 30 cm. If its length is decreased by 3 cm and its width is increased by 5 cm, the area of the rectangle will decrease by 8 cm2. Find the area of the original rectangle.

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Answers (1)

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Yaritza Joyce · Answer 1

Let L be length, W be width

(L-4) = (W+5)

(L-4) (W+5) = LW+40

simplify the first equation: L-W=5

simplify the second equation: (L-4) (W+5) = LW+40

LW-4W+5L-20=LW+40 = >5L-4W=60

solve this system of equations: L-W=9

5L-4W=60

you get W=15, L=24, so the area is 24*15=360

#3:

(L-3) (W+5) = LW-8

2L=2W=30

W=68/8=8.5, L=52/8=6.5, LW=55.25