Question

The ratio of length and breadth of the rectangle are in the ratio of 3;2 the respective ratio of its perimeter are 5:9what is the breadth of the rectangle in meters

Answer 1

Correct question: The ratio of length and breadth of a rectangle is 3:2 respectively. the respective ratio of it's perimeter and area is 5:9. What is the breadth of the rectangle in meters?

Given:

• Ratio of length and breadth of rectangle is 3:2.
• Ratio of perimeter and area of rectangle is 5:9.

To find:

• Breadth of rectangle in the given question.

Answer:

• Breadth of rectangle is 6 meters.

Step-by-step explanation:

Let the length and breadth of rectangle be x.

Therefore,

• Length = 3x
• Breadth = 2x.

Given ratio = 3:2

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1. Formula of Perimeter of rectangle:

                             = 2(l+b)

                             = 2(3x+2x)

                             = 10x

Therefore, Perimeter of rectangle is 10x.

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2. Formula for area of rectangle:

                        = l × b

                        = 3x × 2x

                        = 6x²

Therefore, Area of rectangle is 6x².

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Given that, Ratio of Perimeter and Area of rectangle is 5:9.                

$\frac{10x}{6x^{2} } = \frac{5}{9}$          

OR  

$\frac{5}{3x} = \frac{5}{9}$            

X = 3.

Breadth of rectangle = 2x

                                  = 2 × 3

                                  = 6 m.

Therefore, Breadth of rectangle is 6 meters.

Answer 2

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Given :

• Ratio of length and breadth is 3:2
• Ratio of perimeter and area is 5:9

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To Find :

• Measure of breadth

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Solution :

let the length of rectangle be 3x, And breadth of rectangle be 2x.

As we know that formula for Perimeter of rectangle is :

$\large{\boxed{\sf{Perimeter \: = \: 2(l \: + \: b) }}} \\ \\ \implies {\sf{Perimeter \: = \: 2(3x \: + \: 2x)}} \\ \\ \implies {\sf{Perimeter \: = \: 2(5x)}} \\ \\ \implies {\sf{Perimeter \: = \: 10x}} \\ \\ {\underline{\sf{\therefore \: Perimeter \: of \: Rectangle \: is \: 10x}}}$

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Also formula for Area of rectangle is :

$\large{\boxed{\sf{Area \: = \: l \: \times \: b}}} \\ \\ \implies {\sf{Area \: = \: 3x \: \times \: 2x}} \\ \\ \implies {\sf{Area \: = \: 6x^2}} \\ \\ {\underline{\sf{\therefore \: Area \: of \: Rectangle \: is \: 6 \: x^2}}}$

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As we are given,

$\large{\boxed{\sf{\dfrac{Perimeter}{Area} \: = \: \dfrac{5}{9}}}} \\ \\ \implies {\sf{\dfrac{10x}{6x^2} \: = \: \dfrac{5}{9}}} \\ \\ \implies {\sf{\dfrac{10}{6x} \: = \: \dfrac{5}{9}}} \\ \\ \implies {\sf{6x \: = \: \dfrac{10 \: \times \: 9}{5}}} \\ \\ \implies {\sf{6x \: = \: \dfrac{90}{5}}} \\ \\ \implies {\sf{x \: = \: \dfrac{18}{6}}} \\ \\ \implies {\sf{x \: = \: 3}}$

• Breadth = 2x = 2(3) = 6 units
• Length = 3x = 3(3) = 9 units