Question

determine the lengths of the unknown sides in the following pairs of similar triangles. x = y = (type integers or simplified fractions.)

Explanation:

Step1: Set up proportion for similar - triangles

Since the two triangles are similar, the ratios of their corresponding sides are equal. The ratio of the hypotenuses is $\frac{50}{25}=2$. So, the ratio of the other corresponding sides should also be 2.

Step2: Find the value of $x$

We know that $\frac{14}{x}=2$. Solving for $x$, we get $x=\frac{14}{2}=7$.

Step3: Find the value of $y$

We know that $\frac{48}{y}=2$. Solving for $y$, we get $y = \frac{48}{2}=24$.

Answer:

$x = 7$, $y = 24$