Question

the length of rectangle is twice its breath if the area of the rectangle is 288sqcm find its perimeter​

Answer 1

• Perimeter of the rectangle = 72 cm.

Given :–

• The length of a rectangle is twice it's breadth.
• Area of the rectangle = 288cm².

To Find :–

• Perimeter of the rectangle.

Solution :–

Let,

The breadth of the rectangle be x.

The length of the rectangle be 2x.

First we need to find the length and the breadth of the rectangle.

Given,

Area of the rectangle = 288cm²

length × breadth = 288cm²

$\longmapsto 2x \times x = 288 \: {cm}^{2}$

$\longmapsto{2x}^{2} = 288 \: {cm}^{2}$

$\longmapsto{x}^{2} = \cancel \dfrac{288}{2} \: {cm}^{2}$

$\longmapsto {x}^{2} = 144 \: {cm}^{2}$

$\longmapsto x = \sqrt{144 \: {cm}^{2} }$

$\longmapsto x = 12 \: cm$

So,

• Length = 2x = 2 × 12 = 24cm.

• Breadth = x = 12cm.

Now, we have to find the perimeter of the rectangle,

We know that,

Perimeter of the rectangle = 2(l + b)

Now we have,

• Length = l = 24 cm.
• Breadth = b = 12 cm.

$\longmapsto 2(24 \: cm + 12 \: m)$

$\longmapsto 2(36 \: cm)$

$\longmapsto2 \times 36 \: cm$

$\longmapsto72 \: cm$

Hence,

The perimeter of the rectangle is 72 cm.