Question

what value of x will make \\( \triangle onm \\) similar to \\( \triangle srq \\) by the sas similarity theorem? 16 20 25 50

Explanation:

Step1: Apply SAS similarity theorem ratio

For $\triangle ONM$ and $\triangle SRQ$ to be similar by SAS similarity theorem, the ratio of corresponding sides should be equal. That is $\frac{ON}{SR}=\frac{MN}{QR}$. Given $ON = 8$, $MN=10$, $SR = 20$. Let $QR=x$. So we have the proportion $\frac{8}{20}=\frac{10}{x}$.

Step2: Cross - multiply to solve for $x$

Cross - multiplying gives $8x=20\times10$. Then $8x = 200$. Dividing both sides by 8, we get $x=\frac{200}{8}=25$.

Answer:

25