Question

look at the figure shown below. dora is writing statements as shown below to prove that if segment st is parallel to segment rq, then x = 12. which equation can she use as statement 5? (3x + 24)3x = 85 51 (3x + 24)85 = 51 3x (3x + 24)51 = 3x 85 34 24 = 3x 51

Explanation:

Step1: Identify corresponding sides of similar triangles

Since $\triangle SPT\sim\triangle QPR$, the ratio of corresponding sides are equal. The side $SP = 3x$ and $QP=3x + 24$, and the side $PT = 51$ and $PR=34 + 51=85$.

Step2: Set up proportion equation

The proportion of corresponding sides gives $\frac{QP}{SP}=\frac{PR}{PT}$, which is $\frac{3x + 24}{3x}=\frac{85}{51}$. Cross - multiplying gives $(3x + 24)\times51=3x\times85$.

Answer:

$(3x + 24)\times51=3x\times85$