Question

the triangles below are similar.
image of two triangles: yellow triangle with sides 22, 33, x; orange triangle with sides 10, 12, y
y = ?

Explanation:

Step1: Identify corresponding sides

For similar triangles, corresponding sides are proportional. The side of length 22 in the yellow triangle corresponds to the side of length 10 in the orange triangle, and the side of length 33 in the yellow triangle corresponds to the side of length \( y \) in the orange triangle.

Step2: Set up the proportion

We set up the proportion \(\frac{22}{10}=\frac{33}{y}\) (or equivalently, since we can also check the other pair, but this is a valid proportion for corresponding sides).

Step3: Cross - multiply and solve for \( y \)

Cross - multiplying gives us \( 22y = 33\times10 \).
First, calculate \( 33\times10=330 \). Then, we have the equation \( 22y = 330 \).
To solve for \( y \), divide both sides of the equation by 22: \( y=\frac{330}{22} \).
Simplifying \(\frac{330}{22}\), we can divide numerator and denominator by 11 first: \( 330\div11 = 30 \) and \( 22\div11 = 2 \), so we get \(\frac{30}{2}=15\). Or we can directly divide 330 by 22: \( 330\div22 = 15 \).

Answer:

\( y = 15 \)