Question

A rectangle with perimeter $264cm$ is divided into five congruent rectangles. Find the perimeter of one of the rectangles.

Answer 1

Given: The perimeter of big rectangle $=264cm$

Divided into $5$ congruent rectangles.

Let the length of the small congruent rectangle be ${}^{\prime }{l}^{\prime }.$

and, the breadth of the small congruent rectangle be ${}^{\prime }{b}^{\prime }.$

therefore, $2l=3b$ [From figure, opposite sides of rectangle are equal]

Perimeter of big rectangle $=4l+5b$

so, $4l+5b=264$

$\Rightarrow 2\left(2l\right)+5b=264$

$\Rightarrow 2\times 3b+5b=264$

$\Rightarrow b=\frac{264}{11}=24cm$

then, $l=\frac{3}{2}b=\frac{3}{2}\times 24=36cm$

$\therefore$ Perimeter of one small congruent rectangle $=2(l+b)=2(36+24)=120cm$