Question

The width of a rectangle is three-fourths the length. If the perimeter is $84cm$, find the length and width of the rectangle.

Answer 1

Let the length of the rectangle be $l$ and the breadth be $b$.

Given:$b=\frac{3}{4}l$

Perimeter$=2(l+b)=84$cm

$\Rightarrow l+b=\frac{84}{2}=42$cm

$\Rightarrow l+\frac{3}{4}l=42$cm since $b=\frac{3}{4}l$

$\Rightarrow \frac{4l+3l}{4}=42$

$\Rightarrow \frac{7l}{4}=42$

$\Rightarrow l=6\times 4=24$cm

$\therefore$ Breadth$=b=\frac{3}{4}l=\frac{3}{4}\times 24=18$cm

$\therefore$ length$=24$cm and width or breadth$=b=18$cm