The area of a triangular field whose sides are 65 m, 72 m, and 97 m is equal to the area of a rectangular park whose sides are in the ratio of 5 : 13. What is the perimeter (in m ) of the rectangular park?
Answer & explanation
Correct answer: option 3
We know that,
Area of triangle = \(\frac{1}{2}\) × base × height
Area of rectangle = length × breadth
Perimeter of rectangle = 2(l + b)
Given,
Length of triangle = 97 m
Base of a triangle =65 m
Height of triangle = 72 m
Ratio of length and breadth of a rectangle = 5 : 13
According to the question
= (\(\frac{1}{2}\) × 65 × 72) = (5x × 13x)
= (65 × 36) = 65x2
= x2 = (\(\frac{(65 × 36) }{65}\)
= x2 = 36
= x = 6 m
So the perimeter of rectangle = 2(5x + 13x)
= (2 × 18x) = 36x
= (36 × 6) = 216 m