Two corners of a triangle have angles of #pi / 8 # and # pi / 8 #. If one side of the triangle has a length of #7 #, what is the longest possible perimeter of the triangle?

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Answer 1 · 2018-01-27T04:12:20

Longest possible perimeter of the triangle #P = color(blue)(26.9343)#

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Third angle #C = pi - (pi/8) + (pi/8) = (3pi)/4#

It is an isosceles triangle with sides a, b equal.

Length 7 should correspond to the least angle #(pi/8)#

Therefore, # a / sin A = b/ sin B = c / sin C#

#c / sin ((3pi)/4) = 7 / sin (pi/8) = 7 / sin (pi/8)#

#c = (7 * sin ((3pi)/4)) / sin (pi/8) = 12.9343#

Longest possible perimeter of the triangle

#P = (a + b + c) = 12.9343 + 7 + 7 = color(blue)(26.9343)#