Question

The perimeter of a rectangle is equal to the perimeter of the square of side 15cm. if the side of the rectangle is 20 cm long, what is the breadth ?​

Answer 1

Answer:

$\large{\underbrace{\underline{\bf{Required\;Answer:-}}}}$

$\frak{Given}\begin{cases}\sf{Perimeter\:of\:Square=Perimeter\:of\:Rectangle}\\\sf{Side\:of\:Square=\bf{15\:cm}}\\\sf{Length\:of\:Rectangle=\bf{20\:cm}}\end{cases}$

$\bigstar\;\underline{To\:Find\::}$

The breadth of the rectangle.

$\bigstar\;\underline{Solution\::}$

» In this question we are given that the perimeters of a square and a rectangle are equal.

» We would first find the perimeter of the square, then we would find the perimeter of the rectangle using the given sides.

» After finding the perimeters, we would compare them so as to get the value of length of the rectangle.

◆ Finding the Perimeter of the Square :

We have :

Side of the square = 15 cm.

We know :

$\odot\;\boxed{\sf Perimeter_{\:square}=4\times Side}$

So,

$\colon \rarr \sf \: perimeter _{ \: square} =4 \times 15 \: cm \\ \\ \colon \dashrightarrow \boxed{ \frak{ \pink{perimeter _{ \: square} = 60 \: cm}}}$

◆ Finding the Perimeter of the Rectangle :

We have :

Length = 20 cm.

Let

Breadth = x cm.

We know :

$\odot\;\boxed{\sf Perimeter_{\:rectangle}=2(Length+Breadth) }$

So,

$\colon \rarr \sf \: perimeter _{ \: rectangle} = 2(20 + x) \: cm \\ \\ \colon \dashrightarrow \boxed{ \pink{ \frak{perimeter _{ \: rectangle} = 40 + 2x \: cm}}}$

◆ Finding the Length of the Rectangle :

We have :

Perimeter of Square = 60 cm.

Perimeter of rectangle = 40 + 2x cm.

We know -

$\colon \implies \sf \: perimeter _{ \: square} = perimeter _{ \: rectangle} \\ \\ \colon \implies \sf \: 60 = 40 + 2x \\ \\ \colon \implies \sf \: 60 - 40 = 2x \\ \\ \colon \implies \sf \: \cancel2x = \cancel{20} \\ \\ \colon \dashrightarrow \underline{ \boxed{ \red{ \bf{x} = \frak{10 }}}}$

$\therefore\;\underline{\sf The \:Breadth\:of\:the\:Rectangle\:is\:\bf{10\:cm}}$

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