Question

Which side lengths form a right triangle?​

Answer 1

`\text{A. }3, √(27), 6,\\\text{B. }8, 15, 17,\\\text{C. }5, 5, √(50)`

Explanation:

All right triangles must follow the Pythagorean Theorem
`a^2+b^2=c^2` where
`c` is the hypotenuse of the triangle.

Verify:

`3^2+√(27)^2=6^2\checkmark,\\8^2+15^2=17^2\checkmark,\\5^2+5^2=√(50)^2\checkmark`

Answer 2

Option : A, B, C

Explanation:

To make sure the lengths form sides of a triangle we use Pythagoras theorem:

Square of length of larger side = Sum of square of smaller sides.

`(A) 3, √(27), 6: => 6^2 = 3^2 + (√(27))^2`

`36 = 9 + 27\\36 = 36\\Satisfies \ Pythagoras \ Theorem`

`(B) 8, 15, 17 :=> 17^2 = 15^2 + 8^2`

`289 = 225 + 64 \\289 = 289 \\Satisfies \ the \ condition`

`(C) 5, 5 , √(50) :=> (√(50))^2 = 5^2 +5^2\\`

`50 = 25 + 25 \\50 = 50\\Satisfies \ the \ condition`