Question

The width of a rectangle is one third length if the perimeter is 180 metre find the dimensions of the rectangle​

Answer 1

$\sf\large\underline{Let:}$

$\tt{\implies Length\:_{(rectangle)}=x}$

$\tt{\implies Breadth\:_{(rectangle)}=\dfrac{x}{3}}$

$\sf\large\underline{To\: Find:}$

$\tt{\implies Rectangle\:_{(dimensions)}=?}$

$\sf\large\underline{Solution:}$

• At first we have to find out the value of x to calculate it's dimension of rectangle]

$\sf\large\underline{Formula\:used:}$

$\sf\small{\implies Perimeter\:_{(rectangle)}=2(length+breadth)}$

$\rm{\implies 2\bigg(x+\dfrac{x}{3}\bigg)=180}$

$\rm{\implies \bigg(x+\dfrac{x}{3}\bigg)=90}$

$\rm{\implies \dfrac{3x+x}{3}=90}$

$\rm{\implies \dfrac{4x}{3}=90}$

$\rm{\implies 4x=270}$

$\rm{\implies x=67.5}$

$\sf\large{Hence,}$

$\tt{\implies Length\:_{(rectangle)}=67.5m}$

$\tt{\implies Breadth\:_{(rectangle)}=\dfrac{67.5}{3}}$

$\tt{\implies Breadth\:_{(rectangle)}=22.5m}$

$\sf\large\underline{Verification:}$

$\sf\small{\implies Perimeter\:_{(rectangle)}=2(length+breadth)}$

$\tt{\implies 180=2(67.5+22.5)}$

$\tt{\implies 180=2\times\:90}$

$\tt{\implies 180=180}$

$\sf\large{\implies Hence,\: Verified}$

Answer 2

Dimensions of the rectangle

180