If you know two sides of a right triangle, what formula will help you find the third side?

If you know two sides of a right triangle, what formula will help you find the third side?

• A. A^2 + B^2 = C^2
• B. A^2 - B^2 = C^2
• C. A^2 + B^2 = A^2
• D. 2AB = C

Answer: (A)

The key idea is the Pythagorean theorem: in a right triangle, the sum of the squares of the two legs equals the square of the hypotenuse. This means you can find the third side using a^2 + b^2 = c^2. If you know both legs, the third side (the hypotenuse) is c = sqrt(a^2 + b^2). If you know one leg and the hypotenuse, you can rearrange to find the other leg: a^2 = c^2 − b^2. The other options don’t reflect this true relationship: subtracting squares isn’t the general rule, and 2AB = C is related to area, not side lengths. For example, with legs 3 and 4, the hypotenuse is sqrt(9 + 16) = 5.

The key idea is the Pythagorean theorem: in a right triangle, the sum of the squares of the two legs equals the square of the hypotenuse. This means you can find the third side using a^2 + b^2 = c^2. If you know both legs, the third side (the hypotenuse) is c = sqrt(a^2 + b^2). If you know one leg and the hypotenuse, you can rearrange to find the other leg: a^2 = c^2 − b^2. The other options don’t reflect this true relationship: subtracting squares isn’t the general rule, and 2AB = C is related to area, not side lengths. For example, with legs 3 and 4, the hypotenuse is sqrt(9 + 16) = 5.