Can someone please help me with this question? I really don't get it. Your help would be much appreciated. :) What is the length of CD to the nearest tenth?

5.7

Step-by-step explanation:

The altitude of a right triangle divides it into two smaller triangles, all three of which are similar.

ΔABC ~ ΔADB ~ ΔBDC

Writing and solving a proportion:

AD / BD = BD / CD

(x + 3) / 5 = 5 / (2x + 3)

(x + 3) (2x + 3) = 25

2x² + 9x + 9 = 25

2x² + 9x − 16 = 0

x = [ -9 ± √(81 − 4(2)(-16)) ] / 2(2)

x = [ -9 ± √(81 + 128) ] / 4

x = (-9 ± √209) / 4

x = -5.86 or 1.36

Since x can't be -5.86, x = 1.36.  So the length of CD is:

CD = 2(1.36) + 3

CD = 5.7

.632

step-by-step explanation:

6 * 1/10 = 3/5

3*0.01 = 0.03

3/5 + 0.03 = .63

2*0.002 = .002

.63 + 0.002 = .632