Question

1. there are two similar triangles. one has sides 4 ft, 11 ft, 13 ft, and the corresponding side of the other are 12 ft, x, and y. find x and y.

Explanation:

Step1: Find the scale - factor

The ratio of the corresponding sides gives the scale - factor. The first pair of corresponding sides are 4 ft and 12 ft. The scale - factor $k=\frac{12}{4}=3$.

Step2: Find the value of x

Since the sides of similar triangles are in proportion, and the side of length 11 ft in the first triangle corresponds to x in the second triangle. Using the scale - factor, we have $x = 11\times k$. Substituting $k = 3$, we get $x=11\times3 = 33$ ft.

Step3: Find the value of y

The side of length 13 ft in the first triangle corresponds to y in the second triangle. Using the scale - factor, we have $y = 13\times k$. Substituting $k = 3$, we get $y=13\times3 = 39$ ft.

Answer:

$x = 33$ ft, $y = 39$ ft