Question

1. solve for x (redraw triangles) a=

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), the ratios of corresponding sides are equal. So, $\frac{a}{a + 4}=\frac{12}{18}$.

Step2: Simplify the Ratio

Simplify $\frac{12}{18}$ to $\frac{2}{3}$. So the equation becomes $\frac{a}{a + 4}=\frac{2}{3}$.

Step3: Cross - Multiply

Cross - multiply to get $3a = 2(a + 4)$.

Step4: Expand and Solve

Expand the right - hand side: $3a=2a + 8$. Subtract $2a$ from both sides: $3a-2a=2a + 8-2a$, which gives $a = 8$.

Answer:

8