Given right triangle ABC with altitude BD drawn to hypotenuse AC. If AD = 5
ind AC = 13, what is the length of AB in simplest radical form? (Note: the figure
is not drawn to scale.)

Step-by-step explanation:

Here we have

AD = 5 = a

AC = 13 = c

∴ BC = 13 - 5 = 8

BD = x = √(AB² + BD²) = √(16 + BD²)

8² + BD² = BC²       → BC² - BD² = 64 .......................(1)

13² - x² = BC²          → BC² + x² = 169.........................(2)

x² = 16 + BD²          → x² - BD² = 16.............................(3)

Solving the three equations with three unknowns by subtracting equation (3) from (2) we have;

BC² + BD² = 153...............................................................(4)

Adding equation foru to one give

2BC² = 217

∴ BC² = 217/2

Similarly, BD² = 89/2 and

x² = 121/2

Therefore, x = AB = √(121/2).