Question

Two corners of a triangle have angles of `( pi )/ 2` and `( pi ) / 4`. If one side of the triangle has a length of `8`, what is the longest possible perimeter of the triangle?

Answer 1

`color(green)("Longest possible perimeter " = 11.31 + 8 + 8 = 27.31 " units"`

Explanation:

`hat A = pi/2, hat B = pi/4, hat C = pi - pi/2 - pi/ 4 = pi/ 4`

It's an isosceles right triangle. To get longest perimeter, side 8 should correspond to the least angle `pi/4` and hence sides b, c.

Since it's a right triangle, `a = sqrt(b^2 + c^2) =sqrt (8^2 + 8^2) = 11.31`

`color(green)("Longest possible perimeter " = 11.31 + 8 + 8 = 27.31 " units"`