Question

A rectangle and a square have equal areas. If the length and perimeter of a rectangle are $9$ cm and $26$ cm respectively, then find the perimeter and area of the square.

Answer 1

Let the sides of the rectangle be $l,b.$

Let the side of square be $a.$

So $l=9$, $P_{rect}=26$ cm

$P_{rect}=2(l+b)$

$\Rightarrow 26=2(9+b)$

$\Rightarrow b=4$cm

$A_{rect}=l\times b=9\times 4=36c{m}^2$

Since $A_{rect}=A_{square}$

$\therefore a^2=36c{m}^2$

$\Rightarrow a=6cm$

$P_{square}=4a=24$ cm

$A_{square}=36c{m}^2$.