Question

The side of a square $ABCD$ is $5cm$ and another square $PQRS$ has perimeter equal to $40cm$. Find the ratio of the perimeter of $ABCD$ to perimeter of $PQRS$. Find the ratio of the area $ABCD$ to the area of $PQRS$

Answer 1

$\Rightarrow$ In square ABCD, side of square = 5cm.

$\Rightarrow$ Let $a=5cm$.

$\Rightarrow$ Perimeter of ABCD = $4\times a$

$\Rightarrow$ Perimeter of ABCD = $4\times 5$

$\therefore$ Perimeter of square ABCD = $20cm$. ---- ( 1 )

$\Rightarrow$ Area of square ABCD = $a^2$

$\Rightarrow$ Area of square ABCD = $5^2$

$\therefore$ Area of square ABCD = $25c{m}^2$. ----- ( 2 )

$\Rightarrow$ In square PQRS,

$\Rightarrow$ Perimeter of square PQRS = $40cm$ [Given] --- ( 3 )

$\Rightarrow$ Perimeter of square PQRS = $4\times b$

$\Rightarrow$ $40=4\times a$ [From ( 3 )]

$\therefore$ $b=10cm$

$\Rightarrow$ Area of square PQRS = $b^2$

$\therefore$ Area of square PQRS = $100c{m}^2$ ------ ( 4 )

From ( 1 ) and ( 3 ) we get,

$\Rightarrow$ $\frac{per\left(ABCD\right)}{per\left(PQRS\right)}=\frac{20}{40}=\frac{1}{2}$

From ( 2 ) and ( 4 ) we get,

$\Rightarrow$ $\frac{Ar\left(ABCD\right)}{Ar\left(PQRS\right)}=\frac{25}{100}=\frac{1}{4}$