Question

in each row, use the given side length for δxyz to find the other side lengths of δxyz.
xy\txz\tyz
10\t24\t26
\t36\t
\t\t32.5
7.5\t\t

Explanation:

Step1: Identify similar - triangles ratio

The first - row side - lengths of $\triangle XYZ$ are in the ratio $10:24:26 = 5:12:13$.

Step2: Find sides when $XZ = 36$

Since the ratio is $5:12:13$, if $XZ$ (corresponding to 12 in the ratio) is 36, then the multiplier $k=\frac{36}{12}=3$. So $XY = 5\times3 = 15$ and $YZ=13\times3 = 39$.

Step3: Find sides when $YZ = 32.5$

If $YZ$ (corresponding to 13 in the ratio) is 32.5, then the multiplier $k=\frac{32.5}{13}=2.5$. So $XY = 5\times2.5 = 12.5$ and $XZ = 12\times2.5 = 30$.

Step4: Find sides when $XY = 7.5$

If $XY$ (corresponding to 5 in the ratio) is 7.5, then the multiplier $k=\frac{7.5}{5}=1.5$. So $XZ = 12\times1.5 = 18$ and $YZ = 13\times1.5 = 19.5$.

Answer:

XY	XZ	YZ
12.5	30	32.5
7.5	18	19.5