Calculate the Legs of a Right Isosceles Triangle: Finding Equal Side Lengths

Question

The triangle in the drawing is rectangular and isosceles.

Calculate the length of the legs of the triangle.

00:00 Find the legs of the triangle (AB,CB)

00:03 We'll use the Pythagorean theorem in triangle ABC

00:15 Sides are equal according to the given data

00:20 We'll substitute appropriate values according to the given data and solve for AC

00:34 We'll isolate AC

00:47 And this is the solution to the question

We use the Pythagorean theorem as shown below:

$AC^2+BC^2=AB^2$

Since the triangles are isosceles, the theorem can be written as follows:

$AC^2+AC^2=AB^2$

We then insert the known data:

$2AC^2=(8\sqrt{2})^2=64\times2$

Finally we reduce the 2 and extract the root:

$AC=\sqrt{64}=8$

$BC=AC=8$

8 cm