Question

the triangles are similar. solve for x. (hint: set up the equation as a proportion). 15 20 45 2x + 5

Explanation:

Step1: Set up proportion

Since the triangles are similar, the ratios of corresponding sides are equal. So, $\frac{45}{15}=\frac{2x + 5}{20}$.

Step2: Cross - multiply

$45\times20=15\times(2x + 5)$.
$900 = 30x+75$.

Step3: Solve for x

Subtract 75 from both sides: $900 - 75=30x$, so $825 = 30x$.
Then divide both sides by 30: $x=\frac{825}{30}=\frac{55}{2}=27.5$.

Answer:

$x = 27.5$