In a right triangle with legs of lengths 3 and 4, what is the length of the hypotenuse?

• A. 5
• B. 6
• C. 7
• D. 4

Answer: (A)

The main idea is the relationship in a right triangle: the square of the hypotenuse equals the sum of the squares of the legs. With legs 3 and 4, you compute 3^2 + 4^2 = 9 + 16 = 25. The hypotenuse is the square root of that sum, so its length is 5. The hypotenuse must be longer than either leg, so 4 cannot be the hypotenuse, and 6 or 7 would require larger sums of squares to satisfy the same relationship. Therefore, the hypotenuse length is 5.