Question

What is the perimeter of the triangle shown on the coordinate plane, to the nearest tenth of a unit?

Answer 1

A geometry app shows lengths that add up to 27.4 units.

The Pythagorean theorem can be used to find the lengths of the segments. Each length is the square root of the sum of squares of the difference in x-coordinates and the difference in y-coordinates.

segment AB: length = √(3²+8²) = √73 ≈ 8.544

segment BC: length = √(7²+4²) = √65 ≈ 8.062

segment CA: length = √(10²+4²) = √116 ≈ 10.770

Then the total perimeter is the sum of these lengths:

... 8.544 +8.062 +10.770 = 27.376 ≈ 27.4 . . . . units