Question

The lenght of a rectangle is 20 cm more than its breadth. if the perimeter is 84 cm, find the length of the rectangle

Answer 1

Answer:

Given :-

• The length of a rectangle is 20 cm more than its breadth.
• The perimeter of a rectangle is 84 cm.

To Find :-

• What is the length of the rectangle.

Formula Used :-

$\clubsuit$ Perimeter Of Rectangle Formula :

$\footnotesize \bigstar \: \: \sf\boxed{\bold{\pink{Perimeter_{(Rectangle)} =\: 2(Length + Breadth)}}}\: \: \: \bigstar$

Solution :-

Let,

$\mapsto \bf Breadth_{(Rectangle)} =\: x\: cm$

Given that :

$\bigstar$ The length of a rectangle is 20 cm more than its breadth.

So,

$\mapsto \bf Length_{(Rectangle)} =\: (x + 20)\: cm$

Given :

• Perimeter of a rectangle = 84 cm

According to the question by using the formula we get,

$\footnotesize \implies \bf Perimeter_{(Rectangle)} =\: 2(Length + Breadth)$

$\implies \sf 84 =\: 2\{(x + 20) + x\}$

$\implies \sf 84 =\: 2(x + x + 20)$

$\implies \sf 84 =\: 2(2x + 20)$

$\implies \sf 84 =\: 4x + 40$

$\implies \sf 84 - 40 =\: 4x$

$\implies \sf 44 =\: 4x$

$\implies \sf \dfrac{\cancel{44}}{\cancel{4}} =\: x$

$\implies \sf \dfrac{11}{1} =\: x$

$\implies \sf 11 =\: x$

$\implies \sf\bold{\purple{x =\: 11}}$

Hence, the required length and breadth of the rectangle is :

$\dag$ Breadth Of Rectangle :

$\dashrightarrow \sf Breadth_{(Rectangle)} =\: x\: cm$

$\dashrightarrow \sf\bold{\red{Breadth_{(Rectangle)} =\: 11\: cm}}$

$\dag$ Length Of Rectangle :

$\dashrightarrow \sf Length_{(Rectangle)} =\: (x + 20)\: cm$

$\dashrightarrow \sf Length_{(Rectangle)} =\: (11 + 20)\: cm$

$\dashrightarrow \sf\bold{\red{Length_{(Rectangle)} =\: 31\: cm}}$

$\therefore$ The length of the rectangle is 31 cm .

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VERIFICATION :-

$\leadsto \mathrm{\bold{Perimeter_{(Rectangle)} =\: 2(Length + Breadth)}}$

We get,

• Length = 31 cm
• Breadth = 11 cm
• Perimeter = 84 cm

So, by putting those values we get,

$\leadsto \mathrm{84 =\: 2(31 + 11)}$

$\leadsto \mathrm{84 =\: (2 \times 31) + (2 \times 11)}$

$\leadsto \mathrm{84 =\: 62 + 22}$

$\leadsto \mathrm{\bold{\purple{84 =\: 84}}}$

$\longrightarrow \: \: \: \: \mathrm{\bold{\underline{\red{L.H.S =\: R.H.S}}}}$

HENCE VERIFIED !!