Question #N930
In the figure below, right triangle $ABC$ has a right angle at $C$, and $AC = 6$ and $BC = 8$. What is the length of the hypotenuse $AB$? [asy] draw((0,0)--(8,0)--(0,6)--cycle); draw((0,0)--(8,0),EndArrow); draw((0,0)--(0,6),EndArrow); label("A",(0,0),SW); label("B",(8,0),SE); label("C",(0,6),NW); label("6",(0,3),W); label("8",(4,0),S); [/asy]
A. 10
B. 12
C. 14
D. 16
Correct Answer is: A
Triangle $ABC$ is a right triangle, so we can use the Pythagorean Theorem to find the length of the hypotenuse. The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, we have $AB^2 = AC^2 + BC^2$, so $AB^2 = 6^2 + 8^2 = 36 + 64 = 100$. Taking the square root of both sides, we get $AB = \sqrt{100}$, or $AB = 10$.