Question

The area of a rectangular park is the same as that of a square park. If the side of the square park is 60 m and the length of the rectangular park is 120 m find the breadth of the rectangular park.

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Answer 1

⇝ Given :-

• The area of a rectangular park is the same as that of a square park.

• The side of the square park is 60 m.

• The length of the rectangular park is 120 m.

⇝ To Find :-

• The breadth of the rectangular park.

⇝ Formulae Used :-

❒ Area of Square :

$\large \underbrace{\underline{\text{A}_{ \text{(Square)}} = \text{a}^2}}$

Where

• a = Side Length of the Square

❒ Area of Rectangle :

$\large\underbrace{\underline{\text A_{\text{(Rectangle)}}\text{ = l × b}}}$

Where ,

• l = Length of Rectangle

• b = Breadth of Rectangle

⇝ Solution :-

We Have,

• Side of Square = a = 60 m

Hence,

$\large\text{A}_{ \text{(Square)}} = \text a^2 \\ \\ = 60 \times 60$

$\orange{ \large :\longmapsto  \underline {\boxed{{\bf {A}_{{(Square)}} = { 3600\: {m^2} }} }}}$

Also,

• Length of Rectangle = l = 120 m

• Let Breadth of Rectangle = b meter

Hence,

$\large\text A_{\text{(Rectangle})}\text{ = (120} \times \text {b)}$

$\orange{ \large:\longmapsto \underline {\boxed{{\bf A_{{Rectangle}}{ =120 \:b}} }}}$

⏩ According To Question :

$\large\red{\text{A}_{ \text{(Square)}} = \text A_{\text{(Rectangle)}}}$

$:\longmapsto 3600 = 120\text b$

$:\longmapsto\text b = \cancel\frac{3600}{120}$

$\purple{ \Large :\longmapsto  \underline {\boxed{{\bf b = 30} }}}$

Hence,

$\large\underline{\pink{ \underline{ \pmb{\frak{Breadth \: of \: Rectangle = 30 \: m }}}}}$

Answer 2

Answer:

Given :-

• The area of a rectangular park is the same as that of a square park. If the side of the square park is 60 m and the length of the rectangular park is 120 m.

To Find :-

• What is the breadth of the rectangular park.

Formula Used :-

$\clubsuit$ Area Of Square Formula :

$\footnotesize\mapsto \sf\boxed{\bold{\pink{Area_{(Square)} =\: Side \times Side}}}$

$\clubsuit$ Area Of Rectangle Formula :

$\footnotesize\mapsto \sf\boxed{\bold{\pink{Area_{(Rectangle)} =\: Length \times Breadth}}}$

Solution :-

First, we have to find the area of square :

Given :

• Side = 60 m

According to the question by using the formula we get,

$\implies \sf Area_{(Square)} =\: 60 \times 60$

$\implies \sf\bold{\purple{Area_{(Square)} =\: 3600\: m^2}}$

Now, we have to find the area of rectangle :

Let,

$\leadsto \bf Breadth_{(Rectangle)} =\: x\: m$

Given :

• Length = 120 m

According to the question by using the formula we get,

$\implies \sf Area_{(Rectangle)} =\: 120 \times x$

$\implies \sf\bold{\purple{Area_{(Rectangle)} =\: 120x\: m}}$

Now, we have to find the breadth of the rectangle park :

$\small\longrightarrow \bf Area_{(Square\: Park)} =\: Area_{(Rectangular\: Park)}$

$\longrightarrow \sf 3600 =\: 120x$

$\longrightarrow \sf \dfrac{360\cancel{0}}{12\cancel{0}} =\: x$

$\longrightarrow \sf \dfrac{\cancel{360}}{\cancel{12}} =\: x$

$\longrightarrow \sf 30 =\: x$

$\longrightarrow \sf\bold{\red{x =\: 30\: m}}$

$\bigstar\: \bf Breadth_{(Rectangle)} =\: 30\: m$

${\small{\bold{\underline{\therefore\: The\: breadth\: of\: the\: rectangular\: park\: is\: 30\: m\: .}}}}$