Question

What is the perimeter of a triangle with corners at `(3 ,7 )`, `(1 ,1 )`, and `(4 ,3 )`?

Answer 1

14

Explanation:

Use the distance formula to calculate each side, then add them up for the perimeter.
Side A: (3 ,7 ) to (1 ,1 )
Side B: (1 ,1 ) to (4 ,3 )
Side C: (3,7) to (4,3)

Given the two points (x1, y1) and (x2, y2), the distance between these points is given by the formula:
d = `sqrt((x_2 – x_1)^2 + (y_2 – y_1)^2)`
Side A: `sqrt((1 – 3)^2 + (1 – 7)^2)` ; `sqrt(4 + 36)` ; `sqrt(40)` ; 6.3
Side B: `sqrt((4 – 1)^2 + (3 – 1)^2)` ; `sqrt(9 + 4)` ; `sqrt(13)` ; 3.6
Side C: `sqrt((4 – 3)^2 + (3 – 7)^2)` ; `sqrt(1 + 16)` ; `sqrt(17)` ; 4.1

Perimeter = 6.3 + 3.6 + 4.1 = 14