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

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Two corners of a triangle have angles of $\frac{π}{2}$ $( pi )/ 2$ and $\frac{π}{4}$ $( pi ) / 4$ . If one side of the triangle has a length of $12$ $12$ , 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 $= 41.9706$ $= color(green)(41.9706)$ units.

Explanation:

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The three angles are $\frac{π}{2}, \frac{π}{4}, \frac{π}{4}$ $pi/2, pi/4, pi/4$

It’s an isosceles triangle right triangle with sides in the ratio $1 : 1 : \sqrt{2}$ $1 : 1 : sqrt2$ as the angles are $\frac{π}{4} : \frac{π}{4} : \frac{π}{2}$ $pi/4 : pi/4 : pi/2$ .

To get the longest perimeter, length ‘12’ should correspond to the smallest angle, viz. $\frac{π}{4}$ $pi/4$ .

The three sides are $12, 12, 12 \sqrt{2}$ $12, 12, 12sqrt2$

$i . e . 12, 12, 17.9706$ $i.e. 12, 12, 17.9706$

The longest possible perimeter of the triangle is

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

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

1 Answer

Explanation:

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