Question

use the figure to answer the question. what is the perimeter of triangle pqr? a 5 units b. 10 units c. $sqrt{5}+3sqrt{2}$ units d. $2sqrt{5}+sqrt{10}$ units

Explanation:

Step1: Find length of $PQ$

Use distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. For $P(3,3)$ and $Q(5,2)$, $PQ=\sqrt{(5 - 3)^2+(2 - 3)^2}=\sqrt{4 + 1}=\sqrt{5}$.

Step2: Find length of $QR$

For $Q(5,2)$ and $R(2,1)$, $QR=\sqrt{(2 - 5)^2+(1 - 2)^2}=\sqrt{9+1}=\sqrt{10}$.

Step3: Find length of $PR$

For $P(3,3)$ and $R(2,1)$, $PR=\sqrt{(2 - 3)^2+(1 - 3)^2}=\sqrt{1 + 4}=\sqrt{5}$.

Step4: Calculate perimeter

Perimeter $=PQ + QR+PR=\sqrt{5}+\sqrt{10}+\sqrt{5}=2\sqrt{5}+\sqrt{10}$.

Answer:

D. $2\sqrt{5}+\sqrt{10}$ units