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

`2√(26)\text{ cm}, 2√(6)\text{ cm}`

Explanation:

We are given the following in the question:

Two sides of triangle:

8 cm and
`√(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+(√(40))^2\\x^2 = 64 + 40\\x^2 = 104\\x = √(104)=2√(26)\text{ cm}`

If the third side is not hypotenuse, then

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

Thus, possible third side of triangle are

`2√(26)\text{ cm}, 2√(6)\text{ cm}`