Question

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

• A. $15cm$ and $18cm$
• B. $25cm$ and $15cm$
• C. $8cm$ and $3cm$
• D. $15cm$ and $12cm$

Answer 1

Answer: (B)

$25cm$ and $15cm$

Let width of rectangle be $W$

$\therefore$ length would be $L=2W-5$
If the length is decreased by $5cm$, then new $L1=2W-10cm$

and width is increased by $2cm$, new width $W1=W+2cm$
Given, Perimeter $=74cm$

$=>2(2W-10+W+2)=74$

$=>3W-8=37$

$=>3W=45$

$=>W=15cm$

$=>L=2W-5=2\left(15\right)-5=25cm$