Question Number 134621 by bobhans last updated on 05/Mar/21
$$\mathrm{Geometry} \\ $$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
$${x}={minimum}\:{side}\:{length}\:{of}\:{square} \\ $$$$\mathrm{8}^{\mathrm{2}} +\mathrm{15}^{\mathrm{2}} =\mathrm{17}^{\mathrm{2}} \:\Rightarrow{right}\:{angled}\:{triangle} \\ $$$$\sqrt{\mathrm{15}^{\mathrm{2}} −{x}^{\mathrm{2}} }={x}−\frac{\mathrm{8}}{\mathrm{15}}{x}=\frac{\mathrm{7}}{\mathrm{15}}{x} \\ $$$$\Rightarrow{x}=\frac{\mathrm{15}}{\:\sqrt{\mathrm{1}+\left(\frac{\mathrm{7}}{\mathrm{15}}\right)^{\mathrm{2}} }}\approx\mathrm{13}.\mathrm{59} \\ $$