Applying the Pythagorean theorem to a right triangle with legs 3 and 4 yields a hypotenuse of:

• A. 5
• B. 9
• C. 4
• D. 6

Answer: (A)

In a right triangle, the square of the hypotenuse equals the sum of the squares of the two legs. So with legs 3 and 4, the hypotenuse length c satisfies c^2 = 3^2 + 4^2 = 9 + 16 = 25. Therefore c = sqrt(25) = 5. This is a familiar Pythagorean triple, so the numbers line up neatly.

Other candidate lengths wouldn’t fit the relationship: a hypothetical hypotenuse of 3 would give c^2 = 9, not 25; 4 would give c^2 = 16; 6 would give c^2 = 36. Only 5 makes c^2 equal 25, matching the sum of the squares of the legs.