Question

The breadth of a rectangular plot is one third of its length . If the perimeter of the plot is 240 metres . What is the length of the plot​

Answer 1

$\mathfrak{\large{\underline{\underline{Answer :-}}}}$

The Length is 90m and Breadth is 30m

$\mathfrak{\large{\underline{\underline{Explanation :-}}}}$

Given :

Breadth of the Rectangle = $\dfrac{1}{3}$ of Length

Perimeter = 240m

To find :

The Length of the Rectangle

Solution :

Consider the Length of the Rectangle as x

Consider the Breadth as $\tt{\dfrac{1}{3}x}$

★ We know that :

Perimeter = $\tt{2(length + breadth)}$

$\tt{\implies} \: 2(x + \dfrac{1}{3}x) = 240$

$\tt{\implies} \: 2x+ \dfrac{2}{3}x = 240$

$\tt{\implies} \: \dfrac{6}{3}x+ \dfrac{2}{3}x = 240$

$\tt{\implies} \: \dfrac{8x}{3} = 240$

$\tt{\implies} \: 8x = 240 \times 3$

$\tt{\implies} \: x = \dfrac{720}{8}$

$\tt{\implies} \:x = 90$

$\rule{300}{1}$

★ Value of $\tt{\dfrac{1}{3}x}$

$\tt{\implies} \: \dfrac{1}{3} \times90</p><p>$

$\tt{\implies} \:30$

$\therefore$ The Length is 90m and Breadth is 30m

$\rule{300}{1}$

$\mathfrak{\large{\underline{\underline{Verification :-}}}}$

$\tt{\implies} \:2(30 + 90) = 240$

$\tt{\implies} \:60 + 180 = 240$

$\tt{\implies} \:240 = 240$

$\therefore$ The Length is 90m and Breadth is 30m

Answer 2

Answer :-

Given :-

Perimeter of rectangular plot is 240 m ;

breadth is one-third of its length.

To Find :-

Length of the plot.

Solution :-

Let the length of rectangular plot be x.

$\sf{So,\ Breadth\ = \dfrac{1}{3} x}$

$\star{\sf{We\ know\ that\ :-}}$

$\boxed{\sf{Perimeter\ of\ rectangle\ =\ 2 (Length + Breadth)}}$

$\implies{\sf{2 (Length + Breadth) = 240 m}}$

$\implies{\sf{2 (x + \dfrac{1}{3} x) = 240 m}}$

$\implies{\sf{2x + \dfrac{2x}{3} = 240}}$

$\implies{\sf{\dfrac{6x + 2x}{3} = 240}}$

$\implies{\sf{\dfrac{8x}{3} = 240}}$

$\implies{\sf{8x = 240 \times 3}}$

$\implies{\sf{8x = 720}}$

$\implies{\sf{x = \dfrac{720}{8}}}$

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

So, the length of rectangular plot is 90 m.

So, the breadth = ${\dfrac{1}{3} \times 90}$

$\boxed{\sf{Breadth = 30 m}}$

$\boxed{\sf{Length = 90 m}}$