Question

triangle uvw is similar to triangle xyz. find the measure of side xy. figures are not dra

Explanation:

Step1: Set up proportion

Since $\triangle UVW\sim\triangle XYZ$, the ratios of corresponding - sides are equal. Let the side corresponding to $UV$ be $XY$ and the side corresponding to $UW$ be $XZ$. So, $\frac{UV}{XY}=\frac{UW}{XZ}$.

Step2: Identify side - lengths

We know that $UV = 2$, $UW = 2.4$, and $XZ = 8$. Let $XY=x$. Then the proportion becomes $\frac{2}{x}=\frac{2.4}{8}$.

Step3: Cross - multiply

Cross - multiplying gives us $2.4x=2\times8$.

Step4: Solve for $x$

$2.4x = 16$, so $x=\frac{16}{2.4}=\frac{160}{24}=\frac{20}{3}\approx6.67$.

Answer:

$\frac{20}{3}$