Question

If the length and breadth of a rectangle are in the ratio 5:3 and its perimeter is 144m, find the area of the rectangle.​

Answer 1

Answer :

Area = 1215 m²

Step-by-step explanation :

Given,

•   The length and breadth of a rectangle are in the ratio 5:3

•   The perimeter of the rectangle = 144 m

To find,

   Area of the rectangle = ?

Solution,

Let

• length, l = 5x
• breadth, b = 3x

⇒ Perimeter of the rectangle = 2 (l + b)

        144 = 2(5x + 3x)

        144/2 = 8x

           8x = 72

          x = 72/8

           x = 9

• length = 5x

                   = 5(9)

                   = 45 m

• breadth = 3x

                      = 3(9)

                      = 27 m

⇒ Area of the rectangle = length × breadth

                                          = l × b

                                          = 45 × 27

                                          = 1215 m²

Answer 2

Let :

• Length = x
• Breadth = y

Given :

• Length : Breadth = x : y = 5:3
• Perimeter = 144m

To find : Area of rectangle

Formula used :

• Perimeter of rectangle = 2×(Length + Breadth)
• Area of rectangle = Length × Breadth

Procedure :

• First of all we will find sides of rectangle, as we have been given perimeter and ratio of sides
• Then , find area from side

Solution :

length : breadth = x : y = 5:3

$\implies \:\sf \dfrac{x}{y} = \dfrac{5}{3} \: \\ \\ \implies \sf \: x \: = \dfrac{5y}{3} \: \: \: \: \: ..........equation \: 1$

Perimeter = 2×(x+y)

=> 144 = 2(x+y) ...... equation 2

putting value of x in above equation, we get;

$\implies \sf \: \dfrac{144}{2} = \dfrac{5y}{3} + y \\ \\ \sf \: taking \: lcm \\ \implies \sf \: \frac{144}{2} = \frac{(5y \times 1) + (3 \times y)}{3} \\ \\ \implies \sf \: 72 = \dfrac{8y}{3} \\ \\ \sf \implies y = 72 \times \dfrac{3}{8} \\ \\ \sf \implies \: y = 9 \times 3 = 27m$

putting value of y in equation 1, we get;

$\sf \: x = \dfrac{5y}{3} = \dfrac{5 \times 27}{3} \\ \sf \: x \: = 5 \times 9 = 45m$

Area of rectangle = length× breadth

Area of rectangle = 45 × 27 m²

Area of rectangle = 1215 m²

ANSWER : Area of rectangle = 1215 m²