Maths-

General

Easy

Question

# The length and breadth of a rectangular plot are in the ratio 3: 1 and its perimeter is 128 m. Find the area of the plot ?

## The correct answer is: ∴ Area of the give rectangle is 768 m2.

### Hint:-

Perimeter of a rectangle = 2 (length + breadth)

Area of a rectangle = length × breadth

Step-by-step solution:-

For the given rectangle-

Length : Breadth = 3 : 1

Let x be the common factor.

∴ Length = 3x …............................................ (Equation i)

& Breadth = x …............................................ (Equation ii)

Perimeter of a rectangle = 2 (length + breadth)

∴ Perimeter of a rectangle = 2 (3x + x) ............ (From Equations i & ii)

∴ Perimeter of a rectangle = 2 × 4x

∴ Perimeter of a rectangle = 8x

∴ 128 = 8x ..................... (From given information)

∴ 128 / 8 = x

∴ 16 = x

∴ Length = 3x = 3 × 16 = 48 m ............................ (Equation iii)

& Breadth = x = 16 m ....................................... (Equation iv)

Area of the given rectangle = length × breadth

∴ Area of the given rectangle = 48 ×16

∴ Area of the given rectangle = 768 m^{2}

Final Answer:-

∴ Area of the give rectangle is 768 m^{2}.

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