Whenever someone says right triangle,
always think of [tex]a^{2} + b^{2} =c^{2} [/tex] first.
If the third side is not hypotenuse, it is either [tex]a[/tex] or [tex]b[/tex], and it doesn't matter which one.
let's plug in what we have:
[tex]72^{2} + b^{2} =97^{2} [/tex]
[tex]b^{2} =97^{2} - 72^{2} [/tex]
[tex]b^{2} =9409 - 5184[/tex]
[tex]b = \sqrt{9409 - 5184}[/tex]
[tex]b = \sqrt{4225}[/tex]
[tex]b = 65[/tex]
Therefore, the third base is 65 cm.
Also, by the way, we know that 97cm is the hypotenus, as hypotenuse is always the longest side in right triangles.
