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?](https://www.tinkutara.com/question/Q134621.png)
$$\mathrm{Geometry} \\ $$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 8^2 +15^2 =17^2 ⇒right angled triangle (√(15^2 −x^2 ))=x−(8/(15))x=(7/(15))x ⇒x=((15)/( (√(1+((7/(15)))^2 ))))≈13.59](https://www.tinkutara.com/question/Q134646.png)
$${x}={minimum}\:{side}\:{length}\:{of}\:{square} \\ $$$$\mathrm{8}^{\mathrm{2}} +\mathrm{15}^{\mathrm{2}} =\mathrm{17}^{\mathrm{2}} \:\Rightarrow{right}\:{angled}\:{triangle} \\ $$$$\sqrt{\mathrm{15}^{\mathrm{2}} −{x}^{\mathrm{2}} }={x}−\frac{\mathrm{8}}{\mathrm{15}}{x}=\frac{\mathrm{7}}{\mathrm{15}}{x} \\ $$$$\Rightarrow{x}=\frac{\mathrm{15}}{\:\sqrt{\mathrm{1}+\left(\frac{\mathrm{7}}{\mathrm{15}}\right)^{\mathrm{2}} }}\approx\mathrm{13}.\mathrm{59} \\ $$