Find the perimeter of triangle ABC. Round your answer to the nearest whole number.

Question

Consider Triangle ABC, graphed in the coordinate plane.

Find the perimeter of triangle ABC. Round your answer to the nearest whole number.

the link of the image : drive.google.com/file/d/1Y8ei41wh_biLgQ0EDXzmBbo0b6zfxqSo/view?usp=sharing

Answer 1

The best way to find the perimeter of the triangle is to draw a separate triangle for each of the three sides.

This allows you to find the vertical and horizontal components of distance between the two points, then use the Pythagorean theorem to solve for the direct distance.

I have drawn vertical and horizontal lines connecting point A and point B. This makes it easy to count the vertical and horizontal distance between the two points. Unfortunately, I was not able to attach pictures due to character limits. Now that we have these two measurements, the Pythagorean theorem (a²+b²=c²) can be used to solve for the distance.

3²+5²= c²

c = √34

AB = √34

Now, the same process can be repeated for each of the other sides:

3²+4²=c²

c = √25 = 5

BC = 5

1²+2²=c²

c = √5

AC = √5

Now, to find the total perimeter, we only have to add up the three distances we calculated:

Perimeter = AC + BC + AB

Perimeter = √5 + 5 + √34

^This is the most accurate answer (no rounding)

Perimeter = 2.236 + 5 + 5.831

Perimeter = 13.067

^This is the numeric answer (rounded, so be careful!)