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 $8$ $8$ , 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 $8$ $8$ , what is the longest possible perimeter of the triangle?

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Answer 1 · 2018-04-19T07:50:57

$Longest possible perimeter = 11.31 + 8 + 8 = 27.31 units$ $color(green)("Longest possible perimeter " = 11.31 + 8 + 8 = 27.31 " units"$

Explanation:

$ˆ A = \frac{π}{2}, ˆ B = \frac{π}{4}, ˆ C = π - \frac{π}{2} - \frac{π}{4} = \frac{π}{4}$ $hat A = pi/2, hat B = pi/4, hat C = pi - pi/2 - pi/ 4 = pi/ 4$

It's an isosceles right triangle. To get longest perimeter, side 8 should correspond to the least angle $\frac{π}{4}$ $pi/4$ and hence sides b, c.

Since it's a right triangle, $a = \sqrt{b^{2} + c^{2}} = \sqrt{8^{2} + 8^{2}} = 11.31$ $a = sqrt(b^2 + c^2) =sqrt (8^2 + 8^2) = 11.31$

$Longest possible perimeter = 11.31 + 8 + 8 = 27.31 units$ $color(green)("Longest possible perimeter " = 11.31 + 8 + 8 = 27.31 " units"$

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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 $8$ $8$ , what is the longest possible perimeter of the triangle?

1 Answer

Explanation:

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Two corners of a triangle have angles of π2 ( pi )/ 2 and π4 ( pi ) / 4 . If one side of the triangle has a length of 8 8 , what is the longest possible perimeter of the triangle?

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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 $8$ $8$ , what is the longest possible perimeter of the triangle?