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 will be 74 cm. Find the length and width of the original rectangle.

Answer 1

Let width of the original rectangle = x cm

$\therefore$ Length of the original rectangle = (2x-5) cm

Now, new length of the rectangle = 2x - 5 -5

= (2x - 10) cm

New width of the rectangle = (x+2) cm

New perimeter = 2 [Length + Width]

= 2 [2x-10+x+2]

= 2 [3x - 8]

= (6x-16) cm

Given; new perimeter = 74 cm

$\therefore$ 6x - 16 = 74

$\Rightarrow$ 6x = 74+16

$\Rightarrow$ 6x = 90

$\Rightarrow x=\frac{90}{6}$

$\Rightarrow x=15$

$\therefore$ Length of the original rectangle

= 2x - 5 = 2$\times$15-5

= 30 - 5 = 25 cm

Width of the original rectangle = x = 15 cm