An equilateral triangle is described on the diagonal of a square. What is the ratio of the area of the triangle to that of the square?

Q: An equilateral triangle is described on the diagonal of a square. What is the ratio of the area of the triangle to that of the square?

area of a square = a² sq cm length of the diagonal = 2 a cm area of equilateral triangle with side 2 a = 3 4 * 2 a 2 required ratio = 3 4 * 2 a 2 : a 2 = 3 : 2

1:2
1:3
2:3
3^(1/2) :2

Correct Answer: 3^(1/2) :2

Explanation:

area of a square = a² sq cm

length of the diagonal = $2 a$ cm

area of equilateral triangle with side $2 a$ = $\frac{3}{4} * 2 a 2$
required ratio = $\frac{3}{4} * 2 a 2 : a 2 = 3 : 2$

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