Question

A square and a rectangle have the same perimeter. Calculate the area of the rectangle if the side of the square is 60 cm and the length of the rectangle is 80 cm

Answer 1

Answer:

3200 sq cm

Step-by-step explanation:

Side of square = 60 cm

Length of rectangle = 80 cm

Perimeter of square = Perimeter of rectangle

perimeter of square = 4 x Side

                                 = 4 x 60 cm

                                 = 240 cm

Perimeter of rectangle = 2 x (Length + Breadth) = 240 cm

                                      = 2 x (80 cm + Breadth) = 240 cm

Breadth of rectangle = perimeter / 2 - Length

                                  = 240 cm / 2 - 80 cm

                                  = 120 cm - 80 cm

                                 = 40 cm

Area of rectangle = Length x Breadth

                             = 80 cm x 40 cm

                             = 3200 sq cm (answer)

Answer 2

Answer:

⠀

Given -

• A square and rectangle shares same perimeter
• Side of Square is 60cm
• Length of Rectangle is 80cm

To Find -

• Area of Rectangle
• Breadth of Rectangle

Formulae to be used -

• Perimter of Square = 4 × Side
• Perimeter of Rectangle = 2(l +b)
• Area of Rectangle = lb sq.units

Explaination -

As we've been given the side of the square which is 60cm , the length of the rectangle which is 80cm and said that the perimeter of the square is equal to the perimeter of the rectangle so, let's find the perimeter of the square first so, that We'll know the perimeter of the rectangle. Additionally as we have been provided with the length of the rectangle let's find its breadth using the perimeter and the length and then find its area.

Solution -

First, we will find the perimeter of Square by applying the formula of square.

$\longrightarrow\sf{Perimeter_{(Square)} = 4 \times Side}\\\\ \longrightarrow\sf{Perimeter = 4 \times 60}\\\\ \longrightarrow\sf{Perimeter = 240cm}$

Now, We will find the perimeter of rectangle in order to find the area of Rectangle. But, breadth of rectangle is still not define. So, we will apply the formula of Rectangle to find the required breadth.

$\longrightarrow\sf{2 ( L + B ) = 240cm}\\\\\longrightarrow\sf{2 ( 80 + b ) = 240cm}\\\\ \longrightarrow\sf{160 + 2b = 240cm}\\\\ \longrightarrow \sf{2b =240 - 160} \\\\\longrightarrow \sf{2b = 80}\\\\\longrightarrow\sf{b \: = \dfrac{80}{2} }\\\\ \longrightarrow{\underline{\sf{\red{b= 40cm}}}}$

Now, we have required Breadth and in order, we have to find the area of Rectangle by applying the given formula.

$\longrightarrow\sf{Area_{(Rectangle)} = l\times b\; sq.units}\\\\ \longrightarrow\sf{Area = 80 \times 40} \\\\ \longrightarrow \underline{\sf{ \red{Area = {3200cm}^{2} }}}$

Final Answer -

$\;\;\;\;\;\leadsto$ Hence, the required Breadth is 40 cm and area of Rectangle is 3200cm².

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