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 coordinates of points

Assume $P(3,3)$, $Q(5,2)$, $R(2,1)$.

Step2: Use distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$ for $PQ$

$PQ=\sqrt{(5 - 3)^2+(2 - 3)^2}=\sqrt{4 + 1}=\sqrt{5}$

Step3: Use distance formula for $QR$

$QR=\sqrt{(2 - 5)^2+(1 - 2)^2}=\sqrt{9+1}=\sqrt{10}$

Step4: Use distance formula for $PR$

$PR=\sqrt{(2 - 3)^2+(1 - 3)^2}=\sqrt{1 + 4}=\sqrt{5}$

Step5: 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