Question

the polygons to the right are similar. find the value of each variable.
x =
y =
(simplify your answers.)

Explanation:

Step1: Find the scale factor

Since the polygons are similar, the ratio of corresponding sides is equal. The sides 25 and 50 are corresponding, so the scale factor is $\frac{25}{50}=\frac{1}{2}$.

Step2: Solve for x

The side of length 48 and x are corresponding. Using the scale factor, we have $\frac{x}{48}=\frac{1}{2}$. Cross - multiplying gives $2x = 48$, so $x=\frac{48}{2}=24$.

Step3: Solve for y

The side of length 14 and the side corresponding to y (along with the other sides) use the same scale factor. Wait, actually, the side with length 14 and the side related to y: since the scale factor is $\frac{1}{2}$, and the side opposite (or corresponding) to y and 14? Wait, no, let's re - examine. The two triangles (the smaller one and the larger one) are similar. The legs of the larger triangle: one leg is 48, the other is 14? Wait, no, the smaller triangle has a hypotenuse of 25 and the larger has a hypotenuse of 50. So the scale factor is $\frac{25}{50}=\frac{1}{2}$. For the vertical side: the larger vertical side is 14? Wait, no, maybe the smaller triangle has a vertical side of y and the larger has a vertical side of 14? Wait, no, let's correct. Let's assume the smaller triangle has sides x (horizontal), y (vertical), and hypotenuse 25. The larger triangle has horizontal side 48, vertical side 14, and hypotenuse 50. Since they are similar, the ratio of horizontal sides is $\frac{x}{48}=\frac{25}{50}=\frac{1}{2}$, so $x = 24$ as before. For the vertical sides, $\frac{y}{14}=\frac{25}{50}=\frac{1}{2}$, so $y=\frac{14}{2}=7$.

Answer:

$x = 24$, $y = 7$