Question

The length of a rectangle is 48 m and its perimeter is 150 m. What will be the perimeter of a square whose area is equal to this rectangle?

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Answer 1

Given,

Length of rectangle (Lr)=48 m

Perimeter of rectangle (Pr) = 150 m

Area of square (As)= Area of rectangle (Ar)

To find,

Perimeter of square (Ps)

Solution,

Using the formula,

Perimeter of a rectangle = 2×(L+B)

As it is given, Perimeter of the rectangle (Pr)= 150

⇒Pr=150

⇒2×(Lr+Br)=150

⇒2×(48+Br)=150

⇒48+Br=$\frac{150}{2}$

⇒48+Br=75

⇒Br=75-48

⇒Br=27

Using the formula,

Area of rectangle (Ar) = Lr×Br

⇒Ar=48×27

⇒Ar=1296

∵Area of square (As)= Area of rectangle (Ar)

Using the formula,

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

∴As=1296

⇒$(Side of the square)^{2}$=1296

⇒Side of the square=$\sqrt{1296}$

⇒Side of the square=36

Using the formula,

Perimeter of square (Ps) = 4 × Side of the square

⇒Ps=4×36

⇒Ps=144

Hence, Perimeter of square is 144