Question

A right triangle has leg lengths of 9 units and 12 units. Write an equation that can be

used to determine the length of the hypotenuse, c .

Answer 1

The Pythagorean Theorem

The Pythagorean Theorem:
`a^2+b^2=c^2`

• a and b are the two legs in a right triangle
• c is the hypotenuse (the longest side of a right triangle; opposite the 90° angle
• *keep in mind that this theorem applies only to right triangles

Solving the Question

We're given:

• Legs = 9 units and 12 units
• Hypotenuse = c

Plug these measurements into the Pythagorean theorem:

`a^2+b^2=c^2\\9^2+12^2=c^2`

⇒ Combine like terms:

`81+144=c^2\\c^2=225`

Answer

`c^2=225`