Question

The perimeter of a rectangle is 240 cm and it's length and breadth are in ratio 5 : 3. Find the area of the square​

Answer 1

Given

• The perimeter of a rectangle is 240 cm
• Length and breadth are in the ratio of 5:3

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To Find

• The area of the rectangle

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Solution

First we'll find the value of the length and breadth of the rectangle.

Let the length be 5x and breadth be 3x (We got these values since the length and breadth are in the ratio of 5:3)

Perimeter of Given Rectangle ⇒ 240 cm

Perimeter of Rectangle ⇒ 2 (Length + Breadth)

Length ⇒ 5x

Breadth ⇒ 3x

Let's solve the following equation step-by-step to find the length and breadth.

2 (5x + 3x) = 240

Step 1: Simplify the equation.

⇒ 2 (5x + 3x) = 240

⇒ 2 (5x) + 2 (3x) = 240

⇒ 10x + 6x = 240

⇒ 16x = 240

Step 2: Divide 16 from both sides of the equation.

⇒ 16x ÷ 16 = 240 ÷ 16

⇒ x = 15

∴ Length ⇒ 5x ⇒ 5(15) ⇒ 75 cm

∴ Breadth ⇒ 3x ⇒ 3(15) ⇒ 45 cm

Now with the obtained values of length and breadth we will find the area of the rectangle.

Area of Rectangle ⇒ Length × Breadth

Length ⇒ 75 cm

Breadth ⇒ 45 cm

Area of Rectangle ⇒ 75 × 45

Area of Rectangle ⇒ 3375 cm²

∴ The area of the given rectangle is 3375 cm²

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Answer 2

Answer:

Given :-

• Perimeter of rectangle = 240 cm
• Ratio of length and breadth = 5:3

To Find :-

Area

Solution :-

As we know that

Perimeter = 2(l + b)

Let the ratio be 5x and 3x

$\large \sf \: 240 = 2(5x + 3x)$

$\large \sf \: \dfrac{240}{2} = (5x + 3x)$

$\large \sf \: 120 = 8x$

$\large \sf \: x = \dfrac{120}{8}$

$\large \sf \: x = 15 \: cm$

Dimensions are

$\large \sf \: Length \: = 5(15) = 75$

$\large \sf \: Breadth \: = 3(15) = 45$

Now,

Finding area

$\large \tt \: Area \: = l \times b$

$\large \sf \: Area \: = 75 \times 45$

$\large \sf \: Area = 3375 \: {cm}^{2}$

Learn More :-

Perimeter of square = 4s

Area of Parallelogram = Base × Height

Area of trapezium = ½ × d1 × d2