Mensurationhard · Past Paper
A square and an equilateral triangle have the same perimeter. What is the ratio of their areas?
A9 : 4*sqrt(3)
B3 : 4
Csqrt(3) : 2
D9*sqrt(3) : 16
✓ Correct Answer: A — 9 : 4*sqrt(3)
Let perimeter = 12x. Square side = 3x, Area = 9x^2. Triangle side = 4x, Area = (sqrt(3)/4)*16x^2 = 4*sqrt(3)x^2. Ratio = 9 : 4*sqrt(3).
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