Question

Which side lengths form a right triangle? Choose all answers that apply: Choose all answers that apply: (Choice A) A 2, 2, \sqrt42,2, 4 ? (Choice B) B 9, 40, 419,40,41 (Choice C) C \sqrt5, 10, \sqrt{125} 5 ? ,10, 125 ? Stuck?Watch a video or use a

Answer 1

(B)

Explanation:

The given options are:

A. 2, 2,
`√(42)`

B. 9,40, 41

C.
`√(5),10,√(125)`

In order to prove that the given side lengths form a right triangle, we will satisfy the Pythagoras theorem.

A.
`(√(42))^(2)=(2)^(2)+(2)^(2)`

⇒
`42=4+4`

⇒
`42=8`

which does not satisfy the theorem, thus this option is incorrect.

B.
`(41)^(2)=(9)^(2)+(40)^(2)`

⇒
`1681=1600+81`

⇒
`1681=1681`

which satisfies the theorem, thus this option is correct.

C.
`(√(125))^(2)=(10)^(2)+(√(5))^(2)`

⇒
`125=100+5`

⇒
`125=105`

which does not satisfy the theorem, thus this option is incorrect.