what value of x will make △onm similar to △srq by the sas similarity theorem?\n16\n20\n25\n50

Explanation:

Step1: Identify corresponding sides

For $\triangle ONM$ and $\triangle SRQ$ to be similar by SAS similarity theorem, the ratios of corresponding sides must be equal. The side $ON = 8$ corresponds to $SR=20$, and side $MN = 10$ corresponds to side $RQ=x$.

Step2: Set up proportion

Set up the proportion $\frac{ON}{SR}=\frac{MN}{RQ}$. Substituting the values, we get $\frac{8}{20}=\frac{10}{x}$.

Step3: Cross - multiply

Cross - multiplying gives $8x = 20\times10$.

Step4: Solve for x

$8x=200$, so $x=\frac{200}{8}=25$.

Answer:

C. 25