Question

The ratio amid perimeter as well as breadth of the rectangle has been 5 : 1. in case area of rectangle has been 216 sq. cm what has been length of rectangle?

Answer 1

Let the breadth be x
Let perimeter be 5x
Perimeter = 2(l+b)
5x = 2(l+x)
5x = 2l+2x
3x = 2l
1.5x = l
A/Q lxb = 216cm²
1.5x×x = 216cm²
1.5x² = 216cm²
x² = 144
x = √144 = 12cm
∴ Length = 1.5x = 1.5x12 = 18cm

Answer 2

Answer:

The length of the rectangle is 18 cm.

Step-by-step explanation:

Given : The ratio amid perimeter as well as breadth of the rectangle has been 5 : 1. in case area of rectangle has been 216 sq. cm.

To find : What has been length of rectangle?

Solution :

Let x be the ratio.

The ratio of perimeter and breadth is 5:1

Perimeter of the rectangle is P=2(l+b)

The breadth of the rectangle is x.

The perimeter of the rectangle is $5x=2(l+x)$

$5x=2l+2x$

$2l=3x$

$l=\frac{3}{2}x$

The area of the rectangle is 216 sq.cm.

The area of the rectangle is

$A=l\times b$

$216=\frac{3}{2}x\times x$

$216=\frac{3}{2}x^2$

$x^2=\frac{216\times 2}{3}$

$x^2=144$

$x=\sqrt{144}$

$x=12$

Therefore, the length of the rectangle is

$l=\frac{3}{2}x$

$l=\frac{3}{2}\times 12$

$l=18$

The breadth of the rectangle is 12 cm.

The length of the rectangle is 18 cm.