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 m2
Final Answer:-
∴ Area of the give rectangle is 768 m2.
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