What is the perimeter of a triangle with corners at (7 ,3 ), (9 ,5 ), and (3 ,3 )?

1 Answer
Feb 11, 2018

4 + 2sqrt10 + 2sqrt2 ~= 13.15

Explanation:

Well, perimeter is simply the sum of the sides for any 2D shape.

We have three sides in our triangle: from (3,3) to (7,3); from (3,3) to (9,5); and from (7,3) to (9,5).

The lengths of each are found by Pythagoras' theorem, using the difference between the x and the y coordinates for a pair of points. .

For the first:

l_1 = sqrt((7-3)^2+(3-3)^2) = 4

For the second:

l_2 = sqrt((9-3)^2+(5-3)^2) = sqrt40 = 2sqrt10~= 6.32

And for the final one:

l_3 = sqrt((9-7)^2+(5-3)^2) = sqrt8 = 2sqrt2 ~= 2.83

so the perimeter is going to be

P = l_1 + l_2 + l_3 = 4 + 6.32 + 2.83 = 13.15

or in surd form,

4 + 2sqrt10 + 2sqrt2