In a 45-45-90 triangle with leg length 4, what is the length of the hypotenuse?

In a 45-45-90 triangle with leg length 4, what is the length of the hypotenuse?

• A. 4√2
• B. 4
• C. 8
• D. 2√2

Answer: (A)

In a 45-45-90 triangle, the two legs are equal, and the hypotenuse is longer by a factor of √2. If each leg is 4, multiply by √2 to get the hypotenuse: 4√2. You can also use the Pythagorean theorem: c^2 = 4^2 + 4^2 = 16 + 16 = 32, so c = √32 = 4√2. This length is greater than the legs, as the longest side should be. The other options don’t fit: 4 is a leg, not the hypotenuse; 2√2 is shorter than a leg, so impossible for the hypotenuse; 8 would not come from legs of 4.

In a 45-45-90 triangle, the two legs are equal, and the hypotenuse is longer by a factor of √2. If each leg is 4, multiply by √2 to get the hypotenuse: 4√2. You can also use the Pythagorean theorem: c^2 = 4^2 + 4^2 = 16 + 16 = 32, so c = √32 = 4√2. This length is greater than the legs, as the longest side should be. The other options don’t fit: 4 is a leg, not the hypotenuse; 2√2 is shorter than a leg, so impossible for the hypotenuse; 8 would not come from legs of 4.