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?

1 Answer
Apr 19, 2018

#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"#