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

Question

Accepted Answer

# 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 $B(-1,1)$, $x_1=-1,y_1 = 6,x_2=-1,y_2 = 1$.
$$
\begin{align*}
AB&=\sqrt{(-1+1)^2+(1 - 6)^2}\
&=\sqrt{0+(-5)^2}\
&=5
\end{align*}
$$
Since $AB = AC$, then $AC=5$.
## Step2: Calculate the length of $BC$
For points $B(-1,1)$ and $C(2,2)$, $x_1=-1,y_1 = 1,x_2=2,y_2 = 2$.
$$
\begin{align*}
BC&=\sqrt{(2 + 1)^2+(2 - 1)^2}\
&=\sqrt{3^2+1^2}\
&=\sqrt{9 + 1}\
&=\sqrt{10}
\end{align*}
$$
## Step3: Calculate the perimeter of $\triangle ABC$
The perimeter $P=AB + AC+BC$. Substitute $AB = 5$, $AC = 5$ and $BC=\sqrt{10}$ into the formula.
$$
\begin{align*}
P&=5+5+\sqrt{10}\
&=10+\sqrt{10}
\end{align*}
$$

# Answer:
$10+\sqrt{10}$ units (the third option)

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QUESTION IMAGE

Question

Explanation:

Step1: Calculate the length of \(AB\)

Step2: Calculate the length of \(BC\)

Step3: Calculate the perimeter of \(\triangle ABC\)

Answer: