Question

in the diagram, ab = 10 and ac = 2√10. what is the perimeter of △abc?
10 units
10 + 2√10 units
20 units
20 + 2√10 units

Explanation:

Step1: Recall perimeter formula

Perimeter of $\triangle ABC=AB + AC+BC$.

Step2: Calculate length of BC

Using the distance formula for two - points $(x_1,y_1)$ and $(x_2,y_2)$ which is $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. For points $B(-5,-2)$ and $C(5,-2)$, $x_1=-5,y_1 = - 2,x_2=5,y_2=-2$. Then $BC=\sqrt{(5+5)^2+(-2 + 2)^2}=\sqrt{10^2+0^2}=10$.

Step3: Calculate perimeter

Given $AB = 10$ and $AC=2\sqrt{10}$, perimeter $P=AB + AC+BC=10+2\sqrt{10}+10=20 + 2\sqrt{10}$.

Answer:

D. $20 + 2\sqrt{10}$ units