Question

m1t2 question 11 11. given △rst is similar to △uvw with rt = 9 inches, uw = 5.4 inches, and rs = 6 inches. what is the length of uv? show your work. what is the length of line uv? (hint: set up the ratios, use the calculator)

Explanation:

Step1: Set up ratio of corresponding sides

Since $\triangle RST\sim\triangle UVW$, we have $\frac{RS}{UV}=\frac{RT}{UW}$.

Step2: Substitute known values

Substitute $RS = 6$, $RT = 9$, and $UW=5.4$ into the ratio: $\frac{6}{UV}=\frac{9}{5.4}$.

Step3: Cross - multiply

$9\times UV=6\times5.4$.

Step4: Solve for $UV$

$UV=\frac{6\times5.4}{9}=\frac{32.4}{9}=3.6$ inches.

Answer:

$3.6$ inches