Question

The length and breadth of a rectangle is in the ratio of 3 : 1. If its perimeter is 96 m, then what is the length of the rectangle?

A) 36m B) 24m C) 12m D) 48m

Answer 1

Answer:-

$\sf{A) \ 36 \ m \ is \ a \ correct \ option.}$

Given:

• The length and breadth of a rectangle is in the ratio of 3:1.

• It's perimeter is 96 m

To find:

• The length of the rectangle.

Solution:

$\sf{Let \ the \ constant \ be \ x.}$

$\sf{According \ to \ the \ first \ condition.}$

$\sf{\implies{Length (l)=3x}}$

$\sf{\implies{Breadth (b)=x}}$

$\sf{According \ to \ second \ condition.}$

$\sf{2(3x+x)=96}$

$\sf{\therefore{2(4x)=96}}$

$\sf{\therefore{8x=96}}$

$\sf{\therefore{x=\frac{96}{8}}}$

$\boxed{\sf{\therefore{x=12}}}$

$\sf{Length (l)=3(12)=36 \ m}$

$\sf\purple{\tt{\therefore{The \ length \ of \ the \ rectangle \ is \ 36 \ m}}}$

Answer 2

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

• Ratio of Length and breadth is 3:1
• Perimeter of rectangle = 96m

$\large\bf\underline {To \: find:-}$

• length of rectangle

$\huge\bf\underline{Solution:-}$

• Ratio of Length and breadth is 3:1

Let the length be 3x and breadth be x.

≫ Perimeter of rectangle = 96m

$\bf \star \: perimeter \: of \: rectangle = 2(l + b)$

»» 2( 3x + x) = 96

»» 2× 4x = 96

»» 4x = 96/2

»» x = 48/4

»» x = 12

So, we get the Value of x = 12

Therefore,

Breadth of rectangle x = 12Length of rectangle 3x = 3 × 12 = 36

• ≫ Length = 36