Question

Two of the side lengths of a triangle are 8 centimeters and 40−−√ centimeters. Select the possible lengths of the third side that make the triangle a right triangle.

Answer 1

Answer:

$2\sqrt{26}\text{ cm}, 2\sqrt{6}\text{ cm}$

Step-by-step explanation:

We are given the following in the question:

Two sides of triangle:

8 cm and $\sqrt{40}$ cm

Let the third side be x cm.

Pythagoras theorem:

The sum of square of two sides of a right angled triangle is equal to the square of hypotenuse.

If the third side is hypotenuse, then by Pythagoras theorem:

$x^2 = 8^2+(\sqrt{40})^2\\x^2 = 64 + 40\\x^2 = 104\\x = \sqrt{104}=2\sqrt{26}\text{ cm}$

If the third side is not hypotenuse, then

$8^2 = x^2 + (\sqrt{40})^2\\64 = x^2 + 40\\x^2 = 24\\x = \sqrt{24} = 2\sqrt{6}\text{ cm}$

Thus, possible third side of triangle are

$2\sqrt{26}\text{ cm}, 2\sqrt{6}\text{ cm}$