Question

i. Prove that for equilateral triangles, area is proportional to the square of the length of aside. What is the constant of proportionality?

ii For squares, is area proportional to square of the length of a side? If so, what is the constant of proportionality?

Answer 1

i. Δ ABC is an equilateral triangle Consider their sides are ‘a’, Draw a perpendicular line CD to AB from C.

In right-angled triangle ADC, according to the Pythagoras theorem AD² + DC² = AC²

DC² = AC² – AD²

ii. If x be the one side of a square then its area y = x²

Area of the square is proportional to the square of their sides.

Constant of proportionality = 1