Question

if area of a square is equal to area of a rectangle and one side of square is 30cm and the length of rectangle is 50cm find the perimeter of the rectangle.​

Answer 1

Square:

• Side of Square = a= 30cm

Then area of the Square:

= side × side

=${a}^{2}$

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(4,0){2}{\line(0,1){4}}\multiput(0,0)(0,4){2}{\line(1,0){4}}\put(-0.5,-0.5){\bf D}\put(-0.5,4.2){\bf A\ @TheDiamond}\put(4.2,-0.5){\bf C}\put(4.2,4.2){\bf B}\put(1.5,-0.6){\bf\large 30\ cm}\put(4.4,2){\bf\large 30\ cm}\end{picture}$

Area of the Square = 30cm × 30cm

→ Area of Square = 900 ${cm}^{2}$

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Rectangle:

• Given, length = 50cm
• Let the breadth of the rectangle be = b cm

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(5,0){2}{\line(0,1){3}}\multiput(0,0)(0,3){2}{\line(1,0){5}}\put(0.03,0.02){\framebox(0.25,0.25)}\put(0.03,2.75){\framebox(0.25,0.25)}\put(4.74,2.75){\framebox(0.25,0.25)}\put(4.74,0.02){\framebox(0.25,0.25)}\multiput(2.1,-0.7)(0,4.2){2}{\sf\large 50 cm}\multiput(-1.4,1.4)(6.8,0){2}{\sf\large b cm}\put(-0.5,-0.4){\bf A}\put(-0.5,3.2){\bf D}\put(5.3,-0.4){\bf B}\put(5.3,3.2){\bf C}\end{picture}$

Area of a rectangle = length × breadth

→ Area of the rectangle = 50 cm × b

━━━━━━━━━━━━━━━━

Now given,

Area of Square = Area of rectangle

Thus,

→ 900${cm}^{2}$= 50cm × b

→ b= 900 ÷ 50 cm

→ b = 18cm

Perimeter of a rectangle = 2 × (length + breadth)

→ Perimeter= 2×(50 + 18) cm

→ Perimeter = 2× 68cm

→ Perimeter of the rectangle = 136cm.

Answer 2

$\sf \huge \red{Square:}$

Side of Square = a= 30cm

• Then area of the Square= side × side

=a²

Area of the Square = 30cm × 30cm

→ Area of Square = 900cm²

━━━━━━━━━━━━━━━━

$\huge\sf \blue{ Rectangle:}$

Given, length = 50cm

Let the breadth of the rectangle be = b cm

• Area of a rectangle = length × breadth

→ Area of the rectangle = 50 cm × b

━━━━━━━━━━━━━━━━

Now given,

Area of Square = Area of rectangle

Thus,

→ 900cm² = 50cm × b

→ b= 900 ÷ 50 cm

→ b = 18cm

Perimeter of a rectangle = 2 × (length + breadth)

→ Perimeter= 2×(50 + 18) cm

→ Perimeter = 2× 68cm

→ Perimeter of the rectangle=136cm.

$\huge \mathcal{ \fcolorbox{lime}{yellow}{ \pink{ThalaPro}}}$