Find the length of side AB in the right triangle shown.

Side AB is 72 cm long.



Explanation:

To find the length of side AB you have to use this formula:

[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]

*Remember there are two legs (a and b) and a hypotenuse (c) on a triangle. The longest side will be the hypotenuse and the other two will be the legs. For this triangle the hypotenuse is side BC while the legs are sides CA and side AB.

Plug in the numbers into the equation.


[tex] {65}^{2} + {b}^{2} = {97}^{2} [/tex]
For this triangle, you were given the hypotenuse (c) and one leg (a). To find the last length solve the equation and balance it so only b is left, like this:

[tex]4225 + {b}^{2} = 9409[/tex]

[tex]9409 - 4225 = 5184[/tex]

Soo...

[tex] {b}^{2} = 5184[/tex]

Then to get the side length, square root 5184.

[tex] \sqrt{5184} = 72[/tex]

So the length of the last side is 72 cm.