Question

1. the triangles are similar by the aa similarity postulate. find the value of x. 7.5 15 x 18 270 27 12 1.2

Explanation:

Step1: Set up proportion

Since the triangles are similar by AA - similarity, the ratios of corresponding sides are equal. So, we have the proportion $\frac{7.5}{15}=\frac{x}{18}$.

Step2: Cross - multiply

Cross - multiplying gives us $7.5\times18 = 15\times x$.

Step3: Solve for x

First, calculate $7.5\times18=135$. Then, $15x = 135$. Divide both sides by 15: $x=\frac{135}{15}=9$. But it seems there is a mistake above, the correct proportion should be $\frac{7.5}{7.5 + 15}=\frac{x}{18}$. Cross - multiplying: $(7.5+15)x=7.5\times18$. $22.5x = 135$. Then $x=\frac{135}{22.5}=6$. Another way, if we consider the ratio of the smaller side of the smaller triangle to the larger side of the smaller triangle is equal to the ratio of the smaller side of the larger triangle to the larger side of the larger triangle. $\frac{7.5}{15}=\frac{x}{18}$, cross - multiplying gives $15x=7.5\times18$, $x = 9$. Let's assume the correct proportion based on similar - triangle side - length relationships: $\frac{7.5}{15}=\frac{x}{18}$, cross - multiplying: $15x=7.5\times18$, $x=\frac{7.5\times18}{15}=\frac{135}{15}=9$.

Answer:

9