Question

A square and rectangle have the same perimeter. If the length and breadth of the rectangle are 80 cm and 20 cm respectively. Find the side and area of the square.

Answer 1

Given :

• Perimeter of Rectangle is equal to the perimeter of Square .
• Length of Rectangle = 80 cm
• Breadth of Rectangle = 20 cm

$\\ \rule{200pt}{3pt}$

To Find :

• Side of the Square = ?

$\\ \rule{200pt}{3pt}$

Solution :

~ Formula Used :

• Perimeter :

${\pink{\bigstar}} \; \; {\underline{\boxed{\green{\sf{ Perimeter{\small_{(Rectangle)}} = 2(Length + Breadth) }}}}}$

• Perimeter :

${\pink{\bigstar}} \; \; {\underline{\boxed{\green{\sf{ Perimeter{\small_{(Square)}} = 4 \times Side }}}}}$

$\\ \qquad{\rule{150pt}{1pt}}$

~ Calculating the Perimeter of Rectangle :

$\begin{gathered} \implies \sf {Perimeter = 2(Length + Breadth) } \\ \end{gathered}$

$\begin{gathered} \implies \sf {Perimeter = 2(80 + 20) } \\ \end{gathered}$

$\begin{gathered} \implies \sf {Perimeter = 2 \times 100 } \\ \end{gathered}$

$\begin{gathered} \implies {\purple{\qquad{\sf {Perimeter = 200 \; m }}}} \\ \end{gathered}$

$\\ \qquad{\rule{150pt}{1pt}}$

~ Calculating the Side of Square :

$\begin{gathered} \longmapsto \sf {Perimeter{\small_{(Rectangle)}} = Perimeter{\small_{(Square)}} } \\ \end{gathered}$

$\begin{gathered} \dashrightarrow \sf { 200 = 4 \times Side } \\ \end{gathered}$

$\begin{gathered} \dashrightarrow \sf { \dfrac{200}{4} = Side } \\ \end{gathered}$

$\begin{gathered} \dashrightarrow \sf { \cancel\dfrac{200}{4} = Side } \\ \end{gathered}$

$\begin{gathered} \dashrightarrow {\red{\qquad{\sf {Side = 50 \; m }}}} \\ \end{gathered}$

$\\ \qquad{\rule{150pt}{1pt}}$

~ Therefore :

❛❛ Side of the Square is 50 m . ❜❜

$\\ {\underline{\rule{300pt}{9pt}}}$

Answer 2

EXPLANATION

Perimeter of Square = Perimeter of Rectangle

We had to find the side and area of square

length and breadth of rectanlgle = 80cm and 20 cm respectively

we will find the total perimeter of rectangle

=2length + 2breadth

=80+80+20+20

=160+40

=200

Perimeter of rectangle = 200

now we had to find the sides of square

square has 4 sides

square perimeter = rectangle perimeter

= 200/4

=2×100/2×2

=100/2

=2×50/2×1

=50/1

=50

sides of square = 50

=50×50

=2,500

=2,500cm²

or 200.5m²

FINAL ANSWERS

Side of Square = 50cm

Area of Square = 2,500cm² or 200.5m²

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