Question
A right-angled triangle has an
area of 120 m², and the ratio of its base to height is 5:3. The side length of an equilateral triangle is 125% of the average of the base and height of the right-angled triangle. Calculate the perimeter of the equilateral triangle.Solution
ATQ, Base of the right angled triangle = 5b Height of the right angled triangle = 3b Area of the right angled triangle = 120 m (1/2) × 5b × 3b = 120 b2 = 16 b = 4 Base of the right angled triangle = 5 × 4 = 20 m Height of the right angled triangle = 3 × 4 = 12 m Side of the equilateral triangle = (20 + 12)/2 × 125/100 = 16 × 125/100 = 20 m Perimeter of the equilateral triangle = 3 × 20 = 60 m
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