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

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 2

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.

${?a}^{2} + {b}^{2} = {c}^{2}$

${9}^{2} + {b}^{2} = {9 + 3}^{2}$

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

$81 + {b}^{2} = 81 + 54 + 9$

$81 + {b}^{2} = 144$

${b}^{2} = 144 - 81 = 63$

${b}^{2} = \sqrt{53} = b = 7.93$

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

${a}^{2} + {b}^{2} = {c}^{2}$

${9}^{2} + {7.93}^{2} = {c}^{2}$

$81 + 63 = {c}^{2}$

${c}^{2} = 81 + 63 = 144$

$\sqrt{c} = \sqrt{144}$

$c = 12$