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.

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