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The ratio of length and breadth of a rectangle is 3 : 2 respectively. The respective ratio of its perimeter and area is 5 : 9. What is the breadth of the rectangle in metres ?
Answer & Solution
Correct Answer:
Option
A
Let the length and breadth of the rectangle be 3x and 2x respectively
Then,
Perimeter = 2 (3x + 2x) = 10x
And,
Area = (3x × 2x) = 6x2
$$\eqalign{ & \therefore \frac{{10x}}{{6{x^2}}} = \frac{5}{9} \cr & \Rightarrow 30x = 90 \cr & \Rightarrow x = 3 \cr} $$
So, breadth = (2 × 3) m = 6 m
Then,
Perimeter = 2 (3x + 2x) = 10x
And,
Area = (3x × 2x) = 6x2
$$\eqalign{ & \therefore \frac{{10x}}{{6{x^2}}} = \frac{5}{9} \cr & \Rightarrow 30x = 90 \cr & \Rightarrow x = 3 \cr} $$
So, breadth = (2 × 3) m = 6 m
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