Question

A rectangle's length is 5 cm less than twice its width . If the length is decreased by 5 cm and width is increased by 2 cm the perimeter of the resulting rectangle will be 74 cm . Find the length and the width of the original rectangle

Answer 1

let l and b be the length and breadth of the rectangle respectively

according to the question:
l=2b-5

on decreasing length by 5 we get new length as:l-5=2b-5-5=2b-10
and new breadth is b+2

so no 2{(b+2)(+2b-10)}=74
so 3b-8=37
solving this equation we get b=15cm
so l=2(15)-5=25cm

therefore,original length and breadth of the rectangle are 25cm and 15cm respectively.

Answer 2

let the length and breadth of the rectangle be x and y respectively.
from the question :
x=2y-5
the length is decreased by 5 cm = 2y-5-5=2y-10
width increased by 2 cm = y+ 2
∴perimeter of resulting rectangle=74=2(y+2+2y-10)
∴74=2(3y-8)
74=6y-16
∴6y=90
y=15
and x= 2×y - 5
∴x=25
∴the length and breadth of original rectangle = 15cm and 25cm respectively  
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