Question

The perimeter of a rectangle is 128 cm and difference

between length and breadth is 16 cm. Find the

perimeter of the square if its area is equal to five times

the area of the rectangle?​

Answer 1

$\large{\underline{\rm{\purple{\bf{Given:-}}}}}$

Perimeter of the rectangle = 128 cm

Length - Breadth = 16

$\large{\underline{\rm{\purple{\bf{To \: Find:-}}}}}$

The value of length and breadth.

The area of the rectangle.

Area of the square.

Perimeter of the square.

$\large{\underline{\rm{\purple{\bf{Solution:-}}}}}$

Given that,

Perimeter of the rectangle = 128 cm

Let us consider the length to be 'x' and breadth to be 'y'

Then, x - y = 16

$\boxed{\sf Perimeter \: of \: a \: rectangle=2(Length+Breadth)}$

Substituting their values, we get

$\implies \sf 2(x+y)=128$

$\implies \sf 2(16+y+y)=128$

$\implies \sf 16+2y=\dfrac{128}{2}$

$\implies \sf 16+2y=64$

Finding the value of y

$\implies \sf 2y=64-16$

$\implies \sf 2y=48$

$\implies \sf y=\dfrac{48}{2}$

$\implies \sf y=24 \: cm$

Hence the breadth is 24 cm

Length = Breadth + 16

That is, $\sf x=24+16$

$\sf = 40 \: cm$

Therefore,

Length of the rectangle = 40 cm

Breadth of the rectangle = 24 cm

Now, finding the area of the rectangle

$\boxed{\sf Area \: of \: a \: rectangle= Length \times Breadth}$

Substituting their values, we get

Area of the rectangle = $\sf 40 \times 24$

Area of the rectangle = $\sf 960 \: cm^{2}$

Let us consider the side of the square to be 'a'

Given that,

Perimeter of the square = 5 (Area of the rectangle)

$\implies \sf a^{2}= 5 \times 960$

$\implies \sf a^{2}=4800$

$\implies \sf a \approx 69 \: cm$

$\boxed{\sf Perimeter \: of \: a \: square = 4 \times Side}$

Substituting their values,

Perimeter of the square = $\sf 4 \times 69$

Perimeter of the square = $\sf 276 \: cm^{2}$