Which set of side lengths will form a right triangle? 7, 24, 25
5, 11, 13
8, 13, 17
9, 24, 25

Step-by-step explanation:

Hi there!

We can solve this using the Pythagorean Theorem. The Pythagorean Theorem states that in a right triangle, a^2 + b^2 = c^2. We can plug each set of numbers into the equation, one by one, to see if the set of numbers is true in the equation. One thing to note is that the largest number out of the set is always the hypotenuse, or c. The other numbers are the legs (a and b.)

a^2 + b^2 = c^2

(5)^2 + (11)^2 = (13)^2

25 + 121 = 169

146 ≠ 169

Since 146 doesn't equal 169, this is NOT a right triangle

Since 657 doesn't equal 625, this is NOT a right triangle

This equation is true, because 625 = 625. Therefore this IS a right triangle.

check the picture below.

well, the angle at the vertex d is clearly not a right-angle, let's check for the one at the vertex f which does look like,   however if it's indeed, that means ef is perpendicular to df, in which case their slopes will be negative reciprocal of each other.

so the negative reciprocal of the slope of ef is 1, however the slope of df is not 1, is 1/2, so nope, they're not perpendicular lines.