Question

Given right triangle A B C ABC with altitude B D ‾ BD drawn to hypotenuse A C ‾ AC . If A D = 11 AD=11 and A C = 21 , AC=21, what is the length of A B ‾ AB in simplest radical form?

Answer 1

To find the length of AB, we can use the Pythagorean theorem. Substituting the given values and solving the equation, we find that AB = 8√5.

Step-by-step explanation:

To find the length of AB, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (AC) is equal to the sum of the squares of the lengths of the other two sides (AB and BC). So, we have AB^2 + BD^2 = AC^2. Substituting the given values, we get AB^2 + 11^2 = 21^2. Simplifying, we have AB^2 + 121 = 441. Subtracting 121 from both sides, we get AB^2 = 320. Taking the square root of both sides, we get AB = √320. Simplifying further, we get AB = 8√5.