Question

Triangle ABC is an isosceles triangle in which AB = AC. What is the perimeter of △ABC?

5 + StartRoot 10 EndRoot units

StartRoot 10 EndRoot units

10 + StartRoot 10 EndRoot units

15 units

Answer 1

It is definitely B

Explanation:

`10 + √(10) units`

Answer 2

Option C.

Explanation:

Assume that the below figure attached with this question.

Distance formula:

`Distance=√((x_2-x_1)^2+(y_2-y_1)^2)`

From the below figure it is clear that the vertices of triangle are A(-1,6), B(-1,1) and C(2,2).

Using distance formula we get

`AB=√(\left(-1-\left(-1\right)\right)^2+\left(1-6\right)^2)\Rightarrow √(0+25)=5`

Similarly,

`BC=√(\left(2-\left(-1\right)\right)^2+\left(2-1\right)^2)=√(10)`

`AC=√(\left(2-\left(-1\right)\right)^2+\left(2-6\right)^2)=5`

The perimeter of △ABC is

`perimeter=AB+BC+AC`

`perimeter=5+√(10)+5`

`perimeter=10+√(10)`

The perimeter of △ABC is
`10+√(10)`.

Therefore, the correct option is C.