Question

find the length of side x and side y given that the trapezoids are similar. x = □, y = □ (simplify your answers. type integers or decimals )

Explanation:

Step1: Find the scale - factor

Since the trapezoids are similar, we can find the scale - factor by comparing the corresponding vertical sides. Let the scale - factor be $k$. We know that the vertical side of the first trapezoid is $14$ and the vertical side of the second trapezoid is $24.5$. So, $k=\frac{24.5}{14}=\frac{245}{140}=\frac{7}{4} = 1.75$.

Step2: Find the length of side $x$

Side $x$ corresponds to the side of length $12$ in the first trapezoid. Using the scale - factor, we have $x = 12\times k$. Substituting $k = 1.75$, we get $x=12\times1.75 = 21$.

Step3: Find the length of side $y$

Side $y$ corresponds to the side of length $13$ in the first trapezoid. Using the scale - factor, we have $y = 13\times k$. Substituting $k = 1.75$, we get $y=13\times1.75=22.75$.

Answer:

$x = 21$, $y = 22.75$