Question

△bri is similar to △ght. find the length of overline{gt}.

Explanation:

Step1: Identify corresponding sides

Since $\triangle BRI \sim \triangle GHT$, the ratio of corresponding sides is equal. Let's assume $RI$ corresponds to $HT$ and $BI$ corresponds to $GT$. So, $\frac{RI}{HT}=\frac{BI}{GT}$.
Given $RI = 7$, $HT = 4.2$, and $BI = 13.6$.

Step2: Set up the proportion

Substitute the known values into the proportion: $\frac{7}{4.2}=\frac{13.6}{GT}$.

Step3: Solve for $GT$

Cross - multiply: $7\times GT=4.2\times13.6$.
First, calculate $4.2\times13.6 = 57.12$.
Then, $GT=\frac{57.12}{7}=8.16$.

Answer:

The length of $\overline{GT}$ is $8.16$.