Question

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

Explanation:

Step1: Calculate length of AB

Since A(-1,6) and B(-1,1), using the distance formula for points with same x - coordinate $d=\vert y_2 - y_1\vert$. Here $d_{AB}=\vert6 - 1\vert=5$.

Step2: Calculate length of AC

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. For A(-1,6) and C(2,2), $x_1=-1,y_1 = 6,x_2=2,y_2 = 2$. Then $d_{AC}=\sqrt{(2+1)^2+(2 - 6)^2}=\sqrt{9 + 16}=\sqrt{25}=5$.

Step3: Calculate length of BC

For B(-1,1) and C(2,2), $d_{BC}=\sqrt{(2 + 1)^2+(2 - 1)^2}=\sqrt{9+1}=\sqrt{10}$.

Step4: Calculate perimeter of △ABC

The perimeter $P=AB + AC+BC$. Since $AB = 5$, $AC = 5$ and $BC=\sqrt{10}$, $P=5 + 5+\sqrt{10}=10+\sqrt{10}$.

Answer:

$10+\sqrt{10}$ units