Using the Pythagorean Theorem: Isosceles triangle

Examples with solutions for Using the Pythagorean Theorem: Isosceles triangle

The triangle in the drawing is rectangular and isosceles.

Calculate the length of the legs of the triangle.

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

Below is an isosceles right triangle:

What is the value of X?

$\sqrt{128}$

Look at the triangles in the diagram below.

DBC is an isosceles triangle.

AB=13
AC=5

Calculate the length of the legs of triangle DBC.

$6\sqrt{2}$ cm

ABC is a right angled isosceles triangle.

What is the ratio of the length of the hypotenuse to the length of the leg?

$\sqrt{2}:1$

The triangle in the figure is isosceles.

The length of the hypotenuse is $\frac{x+3}{\sqrt{2}}$ cm.

Work out the length of the leg.

$\frac{x+3}{2}$ cm