Question

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

Answer 1

`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`