Question

Based on the side lengths given (a, b, and o, which triangles are right triangles?​

Answer 1

2 & 3

Explanation:

Pythagorean Theorem is
`a^2+b^2=c^2`.

If the values given in each option satisfy the theorem, the sides will make a right triangle.

For Option One:

`4^2+6^2=8^2\\=> 4^2=16\\=> 6^2=36\\=>8^2 =64\\16+36=64\\\boxed{52\\eq 64}`

The sides would not make a right triangle.

For Option Two:

`6^2+8^2=10^2\\=> 6^2 = 36\\=> 8^2=64\\=> 10^2=100\\36+64=100\\\boxed{100=100}`

The sides would make a right triangle.

For Option Three:

`5^2+6^2=√(61)^2\\ => 5^2=25\\=>6^2=36\\=>√(61)^2=61\\ 25+36=61\\\boxed {61=61}`

The sides would make a right triangle.

For Option Four:

`6^2+9^2=12^2\\=> 6^2=36\\=>9^2=81\\=>12^2=144\\36+81=144\\\boxed{117\\eq 144}`

The sides would not make a right triangle.

The correct answer should be options two and three.