Question

question 12 of 50 the value of y is: triangle diagram with segments 10, 15, y, 21 and arrows indicating parallel sides options: 13, 14, none of the choices are correct, 10, 12

Explanation:

Step1: Identify Similar Triangles

The line segment in the triangle is parallel to the base, so the two triangles are similar by the Basic Proportionality Theorem (Thales' theorem). Thus, the sides are proportional.

Step2: Set Up Proportion

The ratio of the corresponding sides should be equal. So, $\frac{10}{10 + 15}=\frac{y}{y + 21}$. Simplify the left - hand side: $\frac{10}{25}=\frac{2}{5}$. So the proportion becomes $\frac{2}{5}=\frac{y}{y + 21}$.

Step3: Cross - Multiply and Solve

Cross - multiply: $2(y + 21)=5y$. Expand the left - hand side: $2y+42 = 5y$. Subtract $2y$ from both sides: $42=5y - 2y=3y$. Then, $y=\frac{42}{3}=14$.

Answer:

14 (and the option corresponding to 14, e.g., if the option is labeled as "14", then the answer is the option with 14. From the given options, it's the option with "14".)