Question

if the area of square is 16m square the area of rectangle is equal to area of square if the length of the rectangle is 8m find the breadth and also find the perimeter of both​

Answer 1

Area of rectangle = Area of square = 16m2

Area of rectangle = Length × Breadth = Length * 8 m = 16m2

L * 8 m = 16m2

Length = 16/8 = 2 m

Perimeter of rectangle = 2(l + b) = 2(8 + 2) = 2(10) = 20 m

Length(a) of side of square = 16/4 = 4 m

Perimeter of square = 4a = 4(4) = 16 m

Answer 2

Concept :-

In the question, it is given that area of the square is given which is equal to area of rectangle and length of the rectangle is also given. By this, we will find  breadth of rectangle and perimeter of the rectangle. Then, the side of the square and area of the square.

Given :-

Area of square = 16 $m^{2}$

Length of the rectangle = 8 m

Formula to be used :-

Area of the rectangle = Length x Breadth

Perimeter of the rectangle = 2(Length + Breadth)

Area of the square = $(side)^{2}$

Perimeter of the square = 4 x side

Solution :-

According to the question,

⇒ Area of square = Area of rectangle

(Substituting the formula of area of rectangle)

⇒ 16 $m^{2}$ = Length x Breadth

⇒ 16 $m^{2}$ = 8 m x Breadth

⇒ Breadth = $\frac{16\:m^{2} }{8m}$

⇒ Breadth = 2 m

Now, finding the perimeter of the rectangle

⇒ Perimeter of the rectangle = 2(Length + Breadth)

⇒ Perimeter of the rectangle = 2(8 m + 2 m)

⇒ Perimeter of the rectangle = 2(10 m)

⇒ Perimeter of the rectangle = 20 m

Now, finding the side of the square.

⇒ Area of square = 16 $m^{2}$

⇒ $(side)^{2}$ = $16 \: m^{2}$

⇒ side = $\sqrt{16 \: m^{2} }$

⇒ side = 4 m

⇒ Perimeter of the square = 4 x side

⇒ Perimeter of the square = 4 x 4 m

⇒ Perimeter of the square = 16 m

Answer :-

Breadth = 2 m

Perimeter of the rectangle = 20 m

Perimeter of the square = 16 m