A triangle has two corners with angles of # pi / 4 # and # pi / 2 #. If one side of the triangle has a length of #7 #, what is the largest possible area of the triangle?

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Answer 1 · 2018-06-02T15:53:18

Largest possible area of the triangle #volor(green)(A_t = 24.5#

#hat A = pi/4, hat B = pi/2, hat C = pi/4#

It’s an isosceles right triangle with sides b & c equal and smaller than a. #:. b = c = 7# to get the largest area.

Side b & c are base & height and a the hypotenuse.

Area of triangle #A_t = (1/2) *b *c = (1/2) * 7 * 7 = 24.5#