Question

The length of a rectangle is twice its width. If its length is decreased by $5cm$ and the width is increased by $5cm,$ the area of the rectangle is increased by $75c{m}^2.$ Find the perimeter of the original rectangle.

• A. $120cm$
• B. None of the above
• C. $240cm$
• D. $210cm$

Answer 1

The correct option is A $120cm$

Let the width of the original rectangle be x.
$\Rightarrow$ Length of the original rectangle $=2x$
Now,
New length of the rectangle $=2x-5$
New width of the rectangle $=x+5$
New area of the rectangle $=$ Original area of the rectangle $+75$
$\Rightarrow (2x–5)\times (x+5)=2x\times x+75$
$\Rightarrow 2x^2+10x–5x–25=2x^2+75$
$\Rightarrow 5x-25=75$
$\Rightarrow 5x=100$
$\Rightarrow x=20cm$

Now,
Perimeter of the original rectangle $=2(2x+x)=2\left(3x\right)=6x=6\times 20=120cm$