Question

In a right-angled triangle, the sum of the squares of the three sides is 72. What is the length of the hypotenuse?

Answer 1

The hypotenuse has a length of 6

Explanation:

Remark

The first step is to create the 2 equations needed to solve this problem.

Then substitute one into the other.

Equations

c^2 + a^2 + b^2 = 72

c^2 = a^2 + b^2

Solution

c^2 + a^2 + b^2 = 72 The sum of the sides each squared of a right triangle = 72

c^2 = a^2 + b^2 The pythagorean theorem says the hypotenuse of the right triangle = the sum of the squares of two smaller sides. You can substitute the hypotenuse squared into the top equation for a^2 + b^2

c^2 + c^2 = 72

2c^2 = 72

c^2 = 36

c = 6. minus 6 is meaningless