ΔXYZ is graphed on the coordinate plane using the following vertices: X(2,7) Y(8,7) Z(5,2). Which of the following is the closest to the perimeter of this triangle? *

Answer 1

This triangle consists a of a flat line across (2,7) to (8,7) along the top. Then the two sides are diagonal down to the point (5,2). We need to find the length of each side and add them together to get perimeter P.

Let’s call

side 1 = (2,7) to (8,7)

side 2 = (8,7) to (5,2)

side 3 = (5,2) to (2,7)

We are going to use the distance formula but in a simpler way.

side length = square root [ (change in x)^2 + (change in y)^2 ]

side 1: x goes from 2 to 8 = change of 6, y goes from 7 to 7 = change of 0

side 1 = square root [ 6^2 + 0^2 ] = square root(36) = 6

side 2: x goes from 8 to 5 = change of 3, y goes from 7 to 2 = change of 5

side 2 = square root [ 3^2 + 5^2 ] = square root(34) or 5.83

side 3: x goes from 5 to 2 = change of 3, y goes form 2 to 7 = change of 5

side 3 = square root [ 3^2 + 5^2 ] = square root(34) or 5.83

Perimeter = side 1 + side 2 + side 3

P = 6 + sqrt(34) + sqrt(34) = 6 + 2sqrt(34)

P = 6 + 5.83 + 5.83 = 17.66