Question

triangle abc is an isosceles triangle in which ab = ac. what is the perimeter of △abc? 3√10 units 10 + √10 units 5 + √10 units 15 units

Explanation:

Step1: Calculate the length of AB

Use the distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. For points $A(-1,6)$ and $B(-1,1)$, $x_1=-1,y_1 = 6,x_2=-1,y_2 = 1$. Then $AB=\sqrt{(-1+1)^2+(1 - 6)^2}=\sqrt{0+( - 5)^2}=5$.

Step2: Calculate the length of AC

For points $A(-1,6)$ and $C(2,2)$, $x_1=-1,y_1 = 6,x_2=2,y_2 = 2$. Then $AC=\sqrt{(2 + 1)^2+(2 - 6)^2}=\sqrt{3^2+( - 4)^2}=\sqrt{9 + 16}=\sqrt{25}=5$.

Step3: Calculate the length of BC

For points $B(-1,1)$ and $C(2,2)$, $x_1=-1,y_1 = 1,x_2=2,y_2 = 2$. Then $BC=\sqrt{(2 + 1)^2+(2 - 1)^2}=\sqrt{3^2+1^2}=\sqrt{9 + 1}=\sqrt{10}$.

Step4: Calculate the perimeter

The perimeter of $\triangle ABC$ is $AB + AC+BC=5 + 5+\sqrt{10}=10+\sqrt{10}$.

Answer:

$10+\sqrt{10}$ units