Question

Which set of three numbers could represent the lengths of the sides of a right triangle?

7, 24, 25
8, 9, 10
9, 11, 14
15, 18, 21

Answer 1

The best way to do this is to take any two numbers, and use the pythagorous theorum to find the other. If the number you get is the last side, then the triangle exists

Example:
\(7,24,25\)
Since the largest number is 25, therefore the hypotnuse is 25

Now, simply sub into the equation, and solve. I will substitue 7 and 24, in hopes I get 25
\[c^2=a^2-b^2\]\[c^2=7^2+24^2\]\[c^2=49+576\]\[c^2=625\]\[c=\sqrt{625}\]\[c=25\]Since the value I got was equal to the number provided, the traingle exists :) Simply do for the rest of the triangles.

Answer 2

so would it be 7,24,25?

Answer 3

Yes :)

Answer 4

But you need to do for all 4

Answer 5

ok i think i understand it, it is just going to take some practice. :)

Answer 6

Thats all it takes :)

Answer 7

ok, so next i would put in 8 and 9 and hope i get 10?

Answer 8

Exactly :)

Answer 9

and if i do get 10 it is correct?

Answer 10

Yes

Answer 11

Note that this only works on right angle trangles

Answer 12

but if i do not get 10 it is incorrect?

Answer 13

ok