Two corners of a triangle have angles of # ( pi )/ 2 # and # ( pi ) / 4 #. If one side of the triangle has a length of # 12 #, what is the longest possible perimeter of the triangle?

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Answer 1 · 2018-01-24T09:09:43

The longest possible perimeter of the triangle is #= color(green)(41.9706)# units.

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The three angles are #pi/2, pi/4, pi/4#

It’s an isosceles triangle right triangle with sides in the ratio #1 : 1 : sqrt2# as the angles are #pi/4 : pi/4 : pi/2#.

To get the longest perimeter, length ‘12’ should correspond to the smallest angle, viz. #pi/4#.

The three sides are #12, 12, 12sqrt2#

#i.e. 12, 12, 17.9706#

The longest possible perimeter of the triangle is

#12 + 12 + 17.9706 = color(green)(41.9706)# units.