Question

if the given triangles are similar, find the missing length.
t 27 u x 3 y
? 45 z
options: 36, 24, 15, 8

Explanation:

Step1: Find the scale factor

The hypotenuse of the smaller triangle is 5, and the hypotenuse of the larger triangle is 45. So the scale factor \( k \) is \( \frac{45}{5} = 9 \).

Step2: Calculate the missing length

The leg of the smaller triangle corresponding to the missing leg is 4. Multiply by the scale factor: \( 4 \times 9 = 36 \).

Answer:

36