In a 45-45-90 triangle, each leg has length 7. What is the length of the hypotenuse? (Enter your answer as a coefficient of √(2); for…

In a 45-45-90 triangle, the legs are equal and the hypotenuse is the leg length times $\sqrt{2}$. With legs of 7, the hypotenuse is $7\sqrt{2}$, so the coefficient is 7. Check with the Pythagorean theorem: $\sqrt{7^2 + 7^2} = \sqrt{98} = 7\sqrt{2}$. A common wrong answer is 14, which comes from adding the legs instead of using the ratio. Another is 2, which is the number inside the radical rather than the number in front of it. A third is 49, from squaring a leg. Keep the radical form and read off the number in front of it.