Question

Find the perimeter of the triangle with these vertices.

(1, 5) , (1, -4), (-4, -4)
Give an exact answer (not a decimal approximation).
Simplify your answer as much as possible.

Answer 1

`\textsf{Perimeter}=14+√(106)`

Explanation:

The perimeter of a two-dimensional shape is the distance all the way around the outside.

Given vertices:

• (1, 5)
• (1, -4)
• (-4, -4)

As vertices (1, 5) and (1, -4) have the same x-coordinate, the measure of the line segment connecting the two points is the difference between their y-coordinates:

`\implies 5-(-4)=9`

As vertices (1, -4) and (-4, -4) have the same y-coordinate, the measure of the line segment connecting the two points is the difference between their x-coordinates:

`\implies 1-(-4)=5`

Finally, to find the measure of the line segment connecting points (1, 5) and (-4, -4), use the distance formula:

`\implies d=√((x_2-x_1)^2+(y_2-y_1)^2)`

`\implies d=√((-4-1)^2+(-4-5)^2)`

`\implies d=√((-5)^2+(-9)^2)`

`\implies d=√(25+81)`

`\implies d=√(106)`

Therefore, the perimeter of the given triangle is the sum of the found side lengths:

`\implies \textsf{Perimeter}=9+5+√(106)`

`\implies \textsf{Perimeter}=14+√(106)`