Question

triangles △qrs and △tuv are similar triangles. their corresponding sides have a ratio of 2 : 5. if the perimeter of △qrs is 22 inches, what is the perimeter of △tuv? a 55 inches b 44 inches c 22 inches d 8.8 inches

Explanation:

Step1: Recall ratio - perimeter relationship

For similar triangles, the ratio of their perimeters is the same as the ratio of their corresponding - side lengths. Let the perimeter of $\triangle QRS$ be $P_1 = 22$ inches, the perimeter of $\triangle TUV$ be $P_2$, and the ratio of corresponding - side lengths be $\frac{a_1}{a_2}=\frac{2}{5}$. Then $\frac{P_1}{P_2}=\frac{2}{5}$.

Step2: Solve for $P_2$

We can cross - multiply the proportion $\frac{P_1}{P_2}=\frac{2}{5}$ to get $2P_2 = 5P_1$. Substitute $P_1 = 22$ into the equation: $2P_2=5\times22$. Then $2P_2 = 110$. Divide both sides by 2: $P_2=\frac{110}{2}=55$ inches.

Answer:

A. 55 inches