Question

the perimeter of a square is 84cm. if the area of the rectangle is 9 cm^2 greater then the area of the given square, find the breadth of the rectangle, if its length is 90cm.​

Answer 1

Given :-

• The perimeter of a square is 84 cm
• The area of the rectangle is 9 cm² greater then the area of the given square
• Length of the rectangle is 90 cm

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To Find :-

• What is the breadth of the rectangle

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Formulas Used :-

♣️ Perimeter Of Square :

$⟹ \: \color{red} \boxed{ \bf Perimeter _{(Square)} \: = \: 4 \times Side}$

♣️Area Of Square :

$⟹ \: \color{red} \boxed{ \bf Area_{(Square)} \: = \: Side \times Side}$

♣️ Area Of Rectangle :

$</strong>⟹<strong> \: \color{</strong><strong>red</strong><strong>} \boxed{ \bf Area_{(Rectangle)} \: = \: Length \times Breadth} </strong><strong>$

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Solution :-

First, We have to find the side of a square :

Given :

• Perimeter of a square = 84 cm

According to question by using formula we get,

$\longmapsto \: \bf Perimeter _{(Square)} \: = \: 4 \times Side$

$\longmapsto \: \: \sf 84 \: cm\: = \: 4 \times Side$

$\displaystyle \longmapsto \: \: \sf \cancel\frac{84}{4} \: = \: Side$

$\displaystyle \longmapsto \: \: \sf \frac{21}{1} \: = \: Side$

$\displaystyle \longmapsto \: \: \sf 21\: = \: Side \:$

$\displaystyle \longmapsto \: \: \bf \red{Side \: = \: 21 \: cm}$

Hence, The side of a square is 21 cm .

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Next, We have to find the area of a square :

Given :

• Side of a square = 21 cm

According to the question by using formula we get,

$\longmapsto \: \bf Area_{(Square)} \: = \: Side \times Side$

$\longmapsto \: \: \sf Area_{(Square)} \: = \: 21 \: cm \times 21 \: cm$

$\longmapsto \: \: \bf \red{Area_{(Square)} \: = \: 441 \: c {m}^{2} }$

Hence, The area of a square is 441 cm² .

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After that, We have to find the area of a rectangle :

Given :

• The area of the rectangle is 9 cm² greater then the area of the given square

Here,

• The area of a square = 441 cm²

So,

The area of a rectangle :

$\longmapsto \: \sf The \: area \: of \: a \: square \: + \: 9 \: {cm}^{2}$

$\longmapsto \: \: \sf 441 \: {cm}^{2} \: + \: 9 \: {cm}^{2}$

$\longmapsto \: \: \bf \red{450 \: {cm}^{2} }$

Hence, The area of a rectangle is 450 cm² .

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Now, We have to find the breadth of a rectangle :

Given :

• Length of a rectangle = 90 cm
• Area of a rectangle = 450 cm²

According to the question by using formula we get,

$\longmapsto \: \bf Area_{(Rectangle)} \: = \: Length \times Breadth$

$\longmapsto \: \: \sf 450 \: {cm}^{2} \: = \: 90 \: cm \times Breadth$

$\displaystyle \longmapsto \: \: \sf \cancel\frac{450}{90} \: = \: Breadth$

$\displaystyle \longmapsto \: \: \sf \frac{5}{1} \: = \: Breadth$

$\displaystyle \longmapsto \: \: \sf 5\: = \: Breadth$

$\displaystyle \longmapsto \: \: \bf \red{ Breadth \: = \: 5 \: cm}$

∴ Hence, the breadth of a rectangle is 5 cm .

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