Question

A rectangle has adjacent sides $8cm$ and $6cm$. The perimeter of the square is equal to the perimeter of this rectangle find the difference between the area of the square and that of rectangle.

• A. $1c{m}^2$
• B. $2c{m}^2$
• C. $3c{m}^2$
• D. $4c{m}^2$

Answer 1

The correct option is A $1c{m}^2$

Area of rectangle $=$ $(8\times 6)=48c{m}^2$
Perimeter of rectangle $=$ $2(8+6)$ $=$ $28cm$
Let the side of square be $a$
Therefore, perimeter $=$ $4a$
Perimeter of square $=$ Perimeter of rectangle
$\Rightarrow 4a=28$
$\Rightarrow a=7cm$
Therefore, area of square $=$ $7^2$ $=$ $49c{m}^2$
Therefore, difference between area of square and area of rectangle=$(49-48)=1c{m}^2$