Question

Which side lengths form a right triangle?​

Answer 1

Answer:

$\text{A. }3, \sqrt{27}, 6,\\\text{B. }8, 15, 17,\\\text{C. }5, 5, \sqrt{50}$

Step-by-step explanation:

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

Verify:

$3^2+\sqrt{27}^2=6^2\checkmark,\\8^2+15^2=17^2\checkmark,\\5^2+5^2=\sqrt{50}^2\checkmark$

Answer 2

Answer:

Option : A, B, C

Step-by-step 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.

$(A) 3, \sqrt{27}, 6: => 6^2 = 3^2 + (\sqrt{27})^2$

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

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

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

$(C) 5, 5 , \sqrt{50} :=> (\sqrt{50})^2 = 5^2 +5^2$

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