Question

the length of a rectangle exceeds its width by 5m. if the width is increased by 1m and the length is decreased by 2m, the area of the new rectangle is 4 sq.m less than the area of the original rectangle. find the dimensions of the original rectangle?

Answer 1

In a rectangle
l = b+5 ------------(2)

In the new rectangle ;
b' = b+1
l' = l-2

Area of new rectangle = area of rectangle-4
l'b' = lb -4

(b+1)(l-2) = lb - 4
lb -2b+l-2 = lb-4
l+2b = -2
l = 2b-2 ------------(1)
______________________
b+5 = 2b-2
5+2 = 2b-1
2b = 8
b = 4 m
_____________________
l =b+5
l = 4+5
l = 9 m
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The dimensions of original rectangle is 4m by 9 m.