Question

Which side lengths form a right triangle? Choose all answers that apply: Choose all answers that apply: (Choice A) A 3, 6, \sqrt{45}3,6, 45 ​ 3, comma, 6, comma, square root of, 45, end square root (Choice B) B \text{2.5, 6, 6.5}2.5, 6, 6.5start text, 2, point, 5, comma, space, 6, comma, space, 6, point, 5, end text (Choice C) C 4, 8, \sqrt{80}4,8, 80 ​

Answer 1

Answer:

A, B and C

Step-by-step explanation:

Given any three side lengths of a right triangle, the longest side is the hypotenuse.

The side lengths  of a right triangle must satisfy the Pythagorean Theorem.

Pythagorean Theorem: $Hypotenuse^2=Opposite^2+Adjacent^2$

Option A: $3, 6, \sqrt{45}$

$(\sqrt{45})^2=3^2+6^2\\45=36+9\\45=45$

True

Option B: 2.5, 6, 6.5

$6.5^2=6^2+2.5^2\\42.25=36+6.25\\42.25=42.25 (TRUE)$

Option C: $4, 8, \sqrt{80}$

$4, 8, \sqrt{80}\\( \sqrt{80})^2=4^2+8^2\\80=16+64\\80=80 (TRUE)$

Since all are true, the side lengths in Options A, B and C forms a right triangle,