Question

A triangle has two corners with angles of `pi / 4` and `pi / 4`. If one side of the triangle has a length of `1`, what is the largest possible area of the triangle?

Answer 1

Largest possible area of the triangle `Delta ABC = (1/2) * 1 * 1 = color (green)(0.5)` sq. units

Explanation:

Three angles are `pi/4, pi/4, (pi-(pi/4 + pi/4)) = pi/2`

It’s an isosceles right triangle with sides in the ratio `1 : 1 : sqrt2`

To get the largest possible area of the triangle, length ‘1’ should correspond to the smallest angle, viz. `pi/4`

Hence the sides are `1, 1, sqrt2`

Largest possible area of the triangle `Delta ABC = (1/2) * 1 * 1 = color (green)(0.5)` sq. units