Calculate Triangle Perimeter: Right Triangle with Sides 7 and 3

Question

Look at the triangle in the figure.

What is its perimeter?

00:00 Calculate the triangle's perimeter

00:05 We'll use the Pythagorean theorem in the triangle

00:12 We'll substitute appropriate values according to the given data and solve for AC

00:27 This is the length of AC

00:32 Now that we have all sides, we can calculate the perimeter

00:35 The perimeter of the triangle equals the sum of its sides

00:41 We'll substitute appropriate values and solve

00:51 And this is the solution to the question

In order to find the perimeter of a triangle, we first need to find all of its sides.

Two sides have already been given leaving only one remaining side to find.

We can use the Pythagorean Theorem.
$AB^2+BC^2=AC^2$
We insert all of the known data:

$AC^2=7^2+3^2$
$AC^2=49+9=58$
We extract the square root:

$AC=\sqrt{58}$
Now that we have all of the sides, we can add them up and thus find the perimeter:
$\sqrt{58}+7+3=\sqrt{58}+10$

$10+\sqrt{58}$ cm