Question

1. given the figure, select the equation that could be used to solve for x. x + 18 2x + 21

Explanation:

Step1: Identify similar - triangles property

Since the lines are parallel (indicated by the equal - segment markings on the base), we can use the property of similar triangles. The ratios of corresponding sides of similar triangles are equal.
The two similar right - triangles have the following ratio of corresponding sides: $\frac{x + 18}{2x+21}= \frac{YP + PI}{PI}=2$ (because $YP = PI$). So the equation is $x + 18=2(2x + 21)$.

Answer:

$x + 18=2(2x + 21)$