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What is the perimeter of a triangle with...

What is the perimeter of a triangle with vertices at coordinates (-2, 3), (4, 3), and (6, -3) ?

A

`4sqrt(11)`

B

`18sqrt(10)`

C

`10+4sqrt(5)`

D

`16+2sqrt(10)`

Text Solution

Verified by Experts

The correct Answer is:
D
Use the distance formula to calculate the lengths between each pair of points. The perimeter of the triangle is the sum of these lengths.
`D_(1)=sqrt((-2-4)^(2)+(3-3)^(2))=sqrt((-6)^(2)+(0)^(2))=sqrt(36)=6`
`D_(2)=sqrt((-2-6)^(2)+(3-(-3))^(2))=sqrt((-8)^(2)+(6)^(2))=`
`sqrt(64+36)=sqrt(100)=10`
`D_(3)=sqrt((4-6)^(2)+(3-(-3))^(2))=sqrt((-2)^(2)+(6)^(2))=`
`sqrt(4+36)=sqrt(40)=2sqrt(10)`
`D_(1)+D_(2)+D_(3)=16+2sqrt(10)`
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