Question

Triangle ABC is an isosceles triangle in which side

AB = AC. What is the perimeter of triangle ABC?
5 + StartRoot 10 EndRoot units
10 + StartRoot 10 EndRoot units
10 StartRoot 10 EndRoot units
50 units

Answer 1

10 + √10 units

Explanation:

Answer 2

Option B.

Explanation:

Consider the below figure attached with this question.

It is given that triangle ABC is an isosceles triangle.

From the below figure it is clear that the vertices of triangle are A(-2,-4), B(2,-1) and C(3,-4).

Distance formula:

`d=√((x_2-x_1)^2+(y_2-y_1)^2)`

Using this formula, we get

`AB=√((2-(-2))^2+(-1-(-4))^2)=√(16+9)=5`

`BC=√((3-2)^2+(-4-(-1))^2)=√(1+9)=√(10)`

`AC=√((3-(-2))^2+(-4-(-4))^2)=√(25)=5`

Now,

Perimeter of triangle ABC = AB + BC + AC

`=5+√(10)+5`

`=10+√(10)`

So, perimeter of triangle ABC is
`10+√(10)` units.

Therefore, the correct option is B.