Question

a rectangle's length is 5 cm less than twice its width. If the length is decreased by 5 cm and the 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 x= Breadth of the rectangle

Then the length of the rectangle $= 2x-5$

Given that "The length is decreased by 5 cm and width is increased by 2cm"

Perimeter of the resulting rectangle = 74 cm

The length is decreased by 5 cm $= 2x-5-5 =2x-10$

The width is increased by 2 cm $= x+2$

Perimeter of the rectangle $= 2(length)+2(width) =74$

$2(2x-10)+2(x+2) = 74$

$4x-20+2x+4 =74$

$6x-16 =74$

$6x= 90$

$x= 15 cm$

Thus the width of the rectangle$= 15 cm$

Length of the rectangle $= 2x-5 =2(15)-5=25 cm$