Question

The respective ratio between length and breadth of a rectangle is 8:5 and its perimeter is 208cm. If the side of the square is 40% less than the breadth of the rectangle, what is the perimeter of the square?

• A. 54cm
• B. 68cm
• C. 88cm
• D. 96cm
• E. 92cm

Answer 1

The correct option is D 96cm

$\frac{Length}{Breadth}=\frac{8}{5}\Rightarrow \frac{l}{b}=\frac{8}{5}$
Let the length of the rectangle (l)=8x
and breadth of the rectangle (b)=5x
According to the question,
2(l+b)=208 (given)
$\Rightarrow 2(8x+5x)=208\Rightarrow 26x=208\Rightarrow x=8cm$
Breadth of the rectangle(b) =5x= $5\times 8$ =40m
Side of the square(s)=40% less of breadth
$\frac{60}{100}\times 40=24cm$
Perimeter of square= $4\times 24cm=96cm$