Answer:
The triple is 9, 12, 15
The hypotenuse is 15.
Step-by-step 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.
Answer:
12 cm
Step-by-step 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.
[tex] {?a}^{2} + {b}^{2} = {c}^{2} [/tex]
[tex] {9}^{2} + {b}^{2} = {9 + 3}^{2} [/tex]
[tex]81 + {b}^{2} = 9(9 + 3) + 3(9 + 3)[/tex]
[tex]81 + {b}^{2} = 81 + 54 + 9[/tex]
[tex]81 + {b}^{2} = 144[/tex]
[tex] {b}^{2} = 144 - 81 = 63[/tex]
[tex] {b}^{2} = \sqrt{53} = b = 7.93[/tex]
so if u found b then u can find c by using the same formula.
[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]
[tex] {9}^{2} + {7.93}^{2} = {c}^{2} [/tex]
[tex]81 + 63 = {c}^{2} [/tex]
[tex] {c}^{2} = 81 + 63 = 144[/tex]
[tex] \sqrt{c} = \sqrt{144} [/tex]
[tex]c = 12[/tex]
