Question

х 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?​

Answer 1

Appropriate 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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Given :–

Length of rectangle = 48 m

Perimeter of rectangle = 150 m

To Find :–

Perimeter of square (whose area is equal to this rectangle)

Solution :–

Rectangle's two opposite sides are equal

so,

48 × 2 = 96

96 - perimeter of rectangle

= 96 - 150

= 54 m

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So , now we can find width of rectangle

Opposite sides are equal

so we will do it like this :–

54 ÷ 2 = 27 m

width = 27m

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Area of rectangle = l × b

= 48 × 27

= 1296 m²

Area of rectangle and square is same

Finding Side of square

Area = 1296

here we can see 1296 is square of 36

you can do it like this also

√1296 = √36×36

so there is pair of 36 and we will take one 36 out

and 36 will be side of square

$\sf\red{Side-}$ 36

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Perimeter of square = 4 × side

= 4 × 36

= 144

$\huge\mathtt\pink{AnSwEr}$

Perimeter of rectangle = 144

Answer 2

Given,

The length of a rectangle is $48m$ and its perimeter is $150m$.

We have to find the breadth of rectangle

Formula,

Perimeter of a rectangle $= 2(l+b)$

Here $l=48m$, and perimeter $=150m$

$150=2(48+b)$

$b=75-48\\b=27$

Therefore, the breadth of the rectangle is $27$.

After that we have to calculate the area of a rectangle

Area of rectangle $= lb$

$=48\times27$

$=1296$

According to the question,

The area of square is equal to the area of a rectangle

So,

$Side^{2}=lb$

$S^{2}=1296$

$S=\sqrt{1296}$

$S=36m$

We have to find the perimeter of a square

Formula,

Perimeter of square $=4\times side$

$=4\times36\\=144$

Therefore, the perimeter of a square is $144m$