Question

Using the image: find the values of x, y, and z

Answer 1

when running a line, in a right-triangle, from the 90° angle perpendicular to its opposite side, we will end up with three similar triangles, one Small, one Medium and a containing Large one. Check the picture below.

`\cfrac{x}{15}=\cfrac{15}{25}\implies \cfrac{x}{15}=\cfrac{3}{5}\implies 5x=45\implies x=\cfrac{45}{5}\implies \boxed{x=9} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{since we know that}}{25=y+x}\implies 25=y+9\implies \boxed{16=y} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{25}{z}=\cfrac{z}{y}\implies \cfrac{25}{z}=\cfrac{z}{16}\implies 400=z^2\implies √(200)=z\implies \boxed{20=z}`