Question

The shortest leg of a right triangle measures 9 centimeters and the hypotenuse measures 3 centimeters more than the longer leg. Find the length of the hypotenuse. Use the Pythagorean Theorem Formula.

I'm not sure how to set this up

Answer 1

12 cm

Explanation:

I don't think u have to use the phytagores theorem b/c the hypotenuse is 9+3=12. but if u have to use this.

`{?a}^(2) + {b}^(2) = {c}^(2)`

`{9}^(2) + {b}^(2) = {9 + 3}^(2)`

`81 + {b}^(2) = 9(9 + 3) + 3(9 + 3)`

`81 + {b}^(2) = 81 + 54 + 9`

`81 + {b}^(2) = 144`

`{b}^(2) = 144 - 81 = 63`

`{b}^(2) = √(53) = b = 7.93`

so if u found b then u can find c by using the same formula.

`{a}^(2) + {b}^(2) = {c}^(2)`

`{9}^(2) + {7.93}^(2) = {c}^(2)`

`81 + 63 = {c}^(2)`

`{c}^(2) = 81 + 63 = 144`

`√(c) = √(144)`

`c = 12`

Answer 2

The triple is 9, 12, 15

The hypotenuse is 15.

Explanation:

Pythagorean Theorem Formula: a²+b²=c² where a & b are the short legs and c is the hypotenuse.

9²+b²=(b+3)²

81+b²=(b+3)²

Small list of the Pythagorean Triples that contain 9:

9,12,15

9,40,41

So as you can see, there are only 2 examples in my list that contain 9 in them. The only one that fits our criteria is the triple, 9, 12 and, 15

You don't need to use the Pythagorean Formula for this as I have just proved.