The area of a triangular field whose sides are 96 m, 110 m, and 146 m is equal to the area of a rectangular park whose sides are in the ratio 3 : 2. What is the perimeter(in m ) of the rectangular park?
Answer & explanation
Correct answer: option 2
We know that,
Area of right triangle = \(\frac{1}{2}\) × base × height
Area of rectangle = length × breadth
Sides of triangular field = 96m, 110m and 146m
Area of triangular field = \(\frac{1}{2}\) × 96 × 110 = 5280 m2
Area of rectangular field = 5280 m2
Let length and breadth of rectangular field be 3a and 2a respectively.
= 3a × 2a = 5280
= a = 4\(\sqrt {55}\) m
Length and breadth of rectangular field = 12\(\sqrt {55}\) m and 8\(\sqrt {55}\) m respectively.
Perimeter of rectangular field = 2 × (12\(\sqrt {55}\) + 8\(\sqrt {55}\)) = 40\(\sqrt {55}\)m