Question

Which side lengths form a right triangle?

Choose all answers that apply:
A
5, V6, V31
B
15, 5,50
C 9, 12,15

Answer 1

`(a)\ 5, \sqrt 6, \sqrt{31`

`(c)\ 9, 12, 15`

Explanation:

Required

Side lengths that form a right triangle

Applying Pythagoras theorem

`a^2 = b^2 + c^2`

Where a is the longest side.

So, we have:

`(a)\ 5, \sqrt 6, \sqrt{31`

`(√(31))^2 = 5^2 + (\sqrt 6)^2`

`31 = 25 + 6`

`31 = 31`

This forms a right triangle

`(b)\ \sqrt 5, \sqrt 5, 50`

`50^2 = (\sqrt 5)^2 + (\sqrt 5)^2`

`2500 = 5 + 5`

`2500 \\e 10`

This does not form a right triangle

`(c)\ 9, 12, 15`

`15^2 = 12^2 + 9^2`

`225 = 144 + 81`

`225 = 225`

This forms a right triangle