Question

the length and breadth of a room are in the ratio 3 ratio 2 if its area is 216 metre square find its perimeter​

Answer 1

$\bf\huge\underline\purple{Answer :-}$

$\large{\boxed{\sf Perimeter \: = 60m}}$

Explanation :-

Given :

• Length and breadth of a room - 3 : 2
• Area of the room - 216 m²

To find :

The perimeter of the room

Solution :-

Let the length of the room be 3x

and the breadth of the room be 2x

We know that,

$\boxed{\sf Area = Length × Breadth}$

According to question,

$= > 3x \times 2x = 216$

$= > 6 {x}^{2} = 216$

$= > {x}^{2} = \dfrac{216}{6}$

$= > {x}^{2} = 36$

$= > x = 6$

$\therefore$The value of x is 6

Now,

The length => 3 × 6 = 18 m

The breadth => 2 × 6= 12 m

We know that,

$Perimeter = 2(length + breadth) unit$

$= 2(18 + 12) \: m$

$= 2 \times 30 \: m$

$= 60 \: m$

Hence, the perimeter of the room is 60 m respectively.

Answer 2

$\underline{\purple{\mathfrak{Answer:-}}}$

$\boxed{perimeter = \red{60m}}$

$\underline{\purple{\mathfrak{Explanation:-:-}}}$

Given

ratio of length and breadth = 3:2

Area = 216 sq.m.

To Find

Perimeter of the room

Solution

Let, the length and breadth of the room are 3x and 2x

We know that

$\boxed{\red{Area = l \times b}}$

on putting values

$\mathsf{(3x)(2x) = 216}$

$\mathsf{6{x}^{2} = 216}$

$\mathsf{{x}^{2} = \dfrac{216}{6}}$

$\mathsf{{x}^{2} = 36}$

$\mathsf{x = \sqrt{36}}$

$\mathsf{x = 6}$

_____________________

$\mathsf{length(l) = 3x}$

$\mathsf{l = 3(6)}$

$\mathsf{l = 18m }$

$\mathsf{breadth(b) = 2x}$

$\mathsf{b = 2(6) }$

$\mathsf{b = 12m }$

____________________

As we know

$\boxed{\red{perimeter= 2(l+b)}}$

on putting values

$\mathsf{\implies 2(18+12) }$

$\mathsf{\implies 2(30)}$

$\mathsf{\implies 60m}$

Hence, perimeter of the room = 60m