Question

Find the perimeter of the triangle with these vertices. (−5,4), (3,1,) ,( −5,1) Give an exact answer (not a decimal approximation). Simplify your answer as much as possible.

Answer 1

The answer to your question is Perimeter = 11 +
`√(73)`

Explanation:

Data

P (-5, 4)

Q (3, 1)

R (-5, 1)

Process

Calculate the distance between the points and sum up the results

a)

dPQ =
`\sqrt{(-5 - 3)^(2) + (4 - 1)^(2)}`

dPQ =
`\sqrt{(-8)^(2) + 3^(2)}`

dPQ =
`√(64 + 9)`

dPQ =
`√(73)`

dQR =
`\sqrt{(-5 - 3)^(2) + (1 - 1)^(2)}`

dQR =
`\sqrt{8^(2)}`

dQR = 8

dPR =
`\sqrt{(-5 + 5)^(2)+ (1 - 4)^(2)}`

dPR =
`\sqrt{3^(2)}`

dPR = 3

b)

Perimeter =
`√(73)` + 8 + 3

Perimeter = 11 +
`√(73)`