Question

What is the perimeter of triangle ABC?

12 units
13 units
14 units
18 units

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Answer 1

Explanation:

Here

• A(-2,6)
• B(1,2)
• C(-2,-2)

Now,

`\\ \tt\hookrightarrow AB=√((-2-1)^2+(6-2)^2)`

`\\ \tt\hookrightarrow AB=√((-3)^2+(4)^2)`

`\\ \tt\hookrightarrow AB=√(9+16)`

`\\ \tt\hookrightarrow AB=√(25)=5units`

And,

`\\ \tt\hookrightarrow BC=√(1+2)^2+(2+2)^2)`

`\\ \tt\hookrightarrow BC=√((3)^2+(4)^2)`

`\\ \tt\hookrightarrow BC=√(9+16)`

`\\ \tt\hookrightarrow BC=√(25)=5units`

And

`\\ \tt\hookrightarrow AC=√((-2+2)^2+(6+2)^2)`

`\\ \tt\hookrightarrow AC=√((0)^2+(8)^2)`

`\\ \tt\hookrightarrow AC=√(8^2)=√(64)=8units`

Now

`\\ \tt\hookrightarrow perimeter=5+5+8=18units`