Question

The ratio of the area of a rectangle to that of a square is $3:2$. The perimeter of the square is $32cm$. The ratio of the breadth to the length of the rectangle is $2:3$. Find the difference between the perimeter of the square and the rectangle.

• A. $34cm$
• B. $8cm$
• C. $12cm$
• D. $20cm$

Answer 1

The correct option is B $8cm$

The perimeter of squire is $32cm$

Then side of square $=\frac{32}{4}=8cm$

Then area of square $=(8{)}^2=64c{m}^2$

The ratio of the area of a rectangle to that of a square is $3:2$

then area of rectangle $=\frac{3}{2}\times 64=96c{m}^2$

Let the length of rectangle angle is $3x$, and breadth is $2x$

Then area of rectangle $=3x\times 2x=96$

$\Rightarrow 6x^2=96\Rightarrow x^2=16\Rightarrow x=4cm$

Then length of rectangle $=3\times 4=12$ and breadth $=2\times 4=8cm$

Then perimeter of rectangle $=2(12+8)=40$

Then difference between the perimeter of the square and the rectangle $=40-32=8cm$