Question

Need Help understanding this math.

Answer 1

1. C is the right angle so AB is the hypotenuse and AD is the altitude to the hypotenuse.

The hypotenuse is

$AB=c= \sqrt{15^2 + 20^2} = \sqrt{5^2(3^2+4^2)} = 25$

The area calculations must match. Let h=CD

$\frac 1 2 a b = \frac 1 2 c h$

$h = \dfrac{ab}{c} = (15)(20)/25 = 12$

Answer: 12

2. This is the same triangle as above. We seek x=AD and DB=25-x

$12^2 + x^2 = 15^2$

$x = \sqrt{3^2(5^2-4^2)} = 9$

AD=9 and DB=25-9=16

Answer: AD=9, DB=16