Question

The breadth of a rectangle is two third its length. If the perimeter is 180 metre find the dimensions of a rectangle.​

Answer 1

Given:-

• Breadth of reactangle is two-thirds its length.
• Perimeter of rectangle = 180 m

To find:-

Dimensions of the rectangle

Assumption:-

Let the length be x

$\sf{breadth = \dfrac{2}{3}rd\: of\: x = \dfrac{2x}{3}}$

Solution:-

We know,

Perimeter of a rectangle = 2(length + breadth)

ATQ,

$\sf{Perimeter = 2(Length + Breadth)\:units}$

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

$\sf{\implies \dfrac{180}{2} = \dfrac{3x+2x}{3}}$

$\sf{\implies 90 = \dfrac{5x}{3}}$

$\sf{\implies 90\times3 = 5x}$

$\sf{\implies x = \dfrac{270}{5}}$

$\sf{\implies x = 54 \:m}$

Therefore,

$\sf{Length = x = 54\:m}$

$\sf{Breadth = \dfrac{2x}{3} = \dfrac{2\times54}{3} = 36\:m}$

Extra Information:-

A rectangle is a shape in which two parallel sides are always equal. All its angles are of 90°.

• $\sf{Area\:of\:rectangle = Length\times Breadth\:\:sq.units}$
• $\sf{Perimeter\:of\:rectangle = 2(Length+Breadth)\:\:units}$