Question

1. the triangles are similar by the aa similarity postulate. find the value of x. 5 70° 3 110° 3 x 2.5 36 10 3.6

Explanation:

Step1: Set up proportion

Since the triangles are similar by AA - similarity postulate, the ratios of corresponding sides are equal. The ratio of the side of length 5 in the larger triangle to the side of length 3 in the larger triangle is equal to the ratio of the side of length $x$ in the smaller triangle to the side of length 3 in the smaller triangle. So, $\frac{5}{3}=\frac{x}{3}$.

Step2: Solve for $x$

Cross - multiply gives $3x = 5\times3$. Then $3x=15$, and dividing both sides by 3, we get $x = 5$. But this is wrong. Let's set up the correct proportion. The correct proportion is based on the fact that if we consider the parallel - side property of similar triangles. The ratio of the non - parallel sides of the two similar triangles gives us $\frac{5}{x}=\frac{3 + 3}{3}$.

Step3: Cross - multiply

Cross - multiplying the proportion $\frac{5}{x}=\frac{6}{3}$ gives us $6x=5\times3$.

Step4: Simplify and solve

$6x = 15$, then $x=\frac{15}{6}=2.5$.

Answer:

2.5