What you have here is a situation with two similar triangles. The triangle in the lower left is similar to the triangle in the upper right - I've included an image with "cutouts" of those triangles so you can see the similarities. Similar triangles have a very important property: the ratios of their corresponding sides are equivalent. Here, we can set up a ratio between the sides of length 64 and x on the larger triangle, and the corresponding sides of length x and 36 on the smaller triangle. Setting the two equal to each other, we have
[tex] \frac{64}{x}= \frac{x}{36} [/tex]
Multiplying both sides of the equation by 36 and x, we get
[tex]64\cdot36=x^2[/tex]
finally, we take the square root of both sides of the equation to find x:
[tex]\sqrt{64\cdot36}=x\\
\sqrt{64}\sqrt{36}=x\\
8\cdot6=x\\
48=x[/tex]
