Question

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

• A. 25 cm
• B. 30 cm
• C. 15 cm
• D. 10 cm

Answer 1

The correct option is A

25 cm

Let the width of the original rectangle be $x$ cm.

$\therefore$ its length = $2x-5$ cm

Length is decreased by 5 $\Rightarrow$ new length = $2x-5-5$ = $2x-10$ cm

Width is increased by 2 $\Rightarrow$ new width = $x+2$ cm

Perimeter of the new rectangle = 74 cm

$\Rightarrow$ $2\times (x+2+2x-10)=74$

$\Rightarrow$ $2\times (3x-8)=74$

$\Rightarrow$ $(6x-16)=74$

$\Rightarrow$ $6x=90$

$\Rightarrow$ $x=15$

Length = $2x-5$ = $(2\times 15)-5=25$ cm