Geometry-If-a-triangle-with-side-lengths-8-15-and-17-can-be-inscribed-in-a-square-what-is-the-minimum-value-of-the-side-length-of-the-square-

Question Number 134621 by bobhans last updated on 05/Mar/21

Geometry

If a triangle with side lengths 8, 15 and 17 can be inscribed in a square, what is the minimum value of the side length of the square?

Answered by mr W last updated on 06/Mar/21

x = m i n i m u m s i d e l e n g t h o f s q u a r e

8^{2} + 15^{2} = 17^{2} \Rightarrow r i g h t a n g l e d t r i a n g l e

\sqrt{15^{2} - x^{2}} = x - \frac{8}{15} x = \frac{7}{15} x

\Rightarrow x = \frac{15}{\sqrt{1 + {(\frac{7}{15})}^{2}}} \approx 13.59

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