Question

the length and breadth of a rectangle are in ratio 3:2 if area of field is 3456m^2 find its length and breadth and hence perimeter​

Answer 1

Answer:

The Perimeter of the rectangle is 240 m.

Step-by-step explanation:

Given :

Ratio of the length to breadth = 3 : 2

Area of the field = 3456 m²

To find :

The Perimeter of the rectangle

Solution :

Let the -

• Length be 3x
• Breadth be 2x

$\bigstar \: \boxed{\sf{Area = Length \times Breadth}}$

$\sf{\implies} \: {3456} = 3x \times 2x \\ \\ \sf{\implies} \: {3456} = 6 {x}^{2} \\ \\ \sf{\implies} \: {x}^{2} = \dfrac{3456}{6} \\ \\ \sf{\implies} \: {x}^{2} = 576 \\ \\ \sf{\implies} \: x = \sqrt{576} \\ \\ \sf{\implies} \: x = 24$

$\rule{300}{1.5}$

★ Length =

$\sf{\implies} \: 3 \times 24 \\ \\ \sf{\implies} \: 72 \: m$

Length = 72 m

$\rule{300}{1.5}$

★ Breadth =

$\sf{\implies} \: 2 \times 24 \\ \\ \sf{\implies} \: 48 \: m$

Breadth = 48 m

$\rule{300}{1.5}$

$\bigstar \: \boxed{\sf{Perimeter = 2(Length + Breadth)}}$

$\sf{\implies} \: 2(72 + 48) \\ \\ \sf{\implies} \: 144 + 96 \\ \\ \sf{\implies} \: 240$

Perimeter = 240 m

$\therefore$ The Perimeter of the rectangle is 240 m.

Answer 2

Answer:

$\large\bold\red{Length=72\:m}\\\\\large\bold\red{Breadth = 48\:m}\\\\\large\bold\red{Perimeter=240\:m}$

Step-by-step explanation:

Given,

A rectangular field having length and breadth in the ratio 3:2.

Let's assume the,

• Length, l = 3x
• Breadth, b = 2x

Also,

Given that,

• Area, a = $3456\:{m}^{2}$

But,

We know that,

• Area of recatangle = Length × Breadth

Therefore,

We get,

$= > lb = 3456 \\ \\ = > 3x \times 2x = 3456 \\ \\ = > 6 {x}^{2} = 3456 \\ \\ = > {x}^{2} = \frac{3456}{6} \\ \\ = > {x }^{2} = 576 \\ \\ = > x = 576 \\ \\ = > x = 24$

Therefore,

• Length = 3 × 24 = 72 m
• Breadth = 2 × 24 = 48 m

Now,

• Perimeter,p = 2( l+ b)

Therefore,

We get,

$= >p = 2(72 + 48 ) \\ \\ = > p = 2 \times 120 \\ \\ = > p = 240$

Therefore,

• Perimeter = 240 m