Question

∆ABC has the points A(1, 7), B(-2, 2), and C(4, 2) as its vertices. What is the measure of the longest side of ∆ABC

Answer 1

The longest side of triangle ABC is BC, which has a length of sqrt(36).

Step-by-step explanation:

Mathematics

To find the measure of the longest side of triangle ABC, we need to calculate the distances between the vertices. Using the distance formula, we can find the lengths of each side:

Side AB = sqrt((x2-x1)^2 + (y2-y1)^2) = sqrt((-2-1)^2 + (2-7)^2) = sqrt(9+25) = sqrt(34)

Side AC = sqrt((x3-x1)^2 + (y3-y1)^2) = sqrt((4-1)^2 + (2-7)^2) = sqrt(9+25) = sqrt(34)

Side BC = sqrt((x3-x2)^2 + (y3-y2)^2) = sqrt((4--2)^2 + (2-2)^2) = sqrt(36+0) = sqrt(36)

Therefore, the longest side of triangle ABC is BC, which has a length of sqrt(36).

Answer 2

AB = sqrt( (-2-1)^2+(2-7)^2)
AB = sqrt 34

BC = sqrt( (-2-4)^2 +(2-2)^2)
BC = sqrt 36

AC = sqrt( (1-4)^2+(7-2)^2)
AC = sqrt 34

BC is the longest side
Sort 36 = 6