Question

The given lengths are two sides of a right triangle. All three side lengths of the triangle are integers, and together they form a Pythagorean triple. Find the length of the third side, then indicate whether it is a leg or a hypotenuse.

28, 96

A.
37, leg
B.
54, leg
C.
92, leg
D.
100, hypotenuse

Answer 1

If the answer is an integer it means you get no decimal answers. So try plugging in these numbers into the Pythagorean Theorem and solve for the missing value. If you get a decimal try another combination.

Answer 2

i tried

Answer 3

Okay try, a and b are the legs. c is the hypotenuse. Let 28=a and 96=b.
Plug them into the Pythagorean Theorem: \[a^2+b^2=c^2\]
Solve for C

Answer 4

ohh ok thanks mate

Answer 5

No problem. Let me know if you need help.

Answer 6

so its 784 for the first one and 9216 for the second one then do u add the together?

Answer 7

them*

Answer 8

Yes add them together. Then you will have to square root them since you have to get rid of the 2 on: \[c^2\]

Answer 9

is it c?
92 leg

Answer 10

No, go back to where you add them.
784+9216=10,000
\[10,000=c^2\]

Answer 11

Then square root both sides. \[\sqrt{10,000}=\sqrt{c^2}\]

Answer 12

k

Answer 13

so the sq root of 10,000 is 100

Answer 14

Correct.

Answer 15

then you multiply?

Answer 16

Nope that will be your final answer.
c=100

c is the hypotenuse of a triangle. So your answer is D.

Answer 17

oh wow thank you so much

Answer 18

Your very welcome. Feel free to ask for any more help if you need it. I will be getting off in 20 minutes but there's plenty of other members to help out.

Answer 19

are you a teacher?

Answer 20

Nope just a student on break. :)