Question

The perimeter of a rectangle is 75 cm. Its length is 11 times its breadth. Find the length and breadth of the rectangle.​

Answer 1

➤ Given :-

Perimeter of the rectangle :- 75 cm

Length of the rectangle :- 11 × Breadth

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➤ To Find :-

Length and breadth of the rectangle

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★ How to do :-

Here, we are given that a rectangle's perimeter measures 75 cm. We are also given that the length is 11 times greater than it's breadth. As we know that the length is always greater than the breadth of the rectangle. In this also the length is 11 times greater than the breadth. We are going to use the concept of transportation of LHS to RHS. And also the formula of the perimetre of rectangle is going to be used.

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➤ Solution :-

${\tt \leadsto 75 = 2 \: (length + breadth)}$

${\tt \leadsto 75 = 2 \: (11x + x)}$

${\tt \leadsto 75 = 2 \: (12x)}$

${\tt \leadsto \dfrac{75}{2} = 12x}$

${\tt \leadsto 37.5 = 12x}$

${\tt \leadsto x = \dfrac{37.5}{12}}$

${\tt \leadsto x = 3.125}$

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Now,

Length of rectangle :-

${\tt \leadsto 3.125 \times 11}$

${\tt \leadsto 34.375 \: \: cm}$

Breadth of rectangle :-

${\tt \leadsto 3.125 \times 1}$

${\tt \leadsto 3.125 \: \: cm}$

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Verification :-

${\tt \leadsto 75 = 2 \: (34.375 + 3.125)}$

${\tt \leadsto 75 = 2 \times 37.5}$

${\tt \leadsto 75 = 75}$

Hence verified !!

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$\Huge\therefore$ The length is 34.375 cm snd the breadth is 3.125.