Question

In the diagram below bc is an altitude of abd.to the nearest whole unit.what is the length of cd

Answer 1

Pythagorean theorem:
                       AB = √30^2 + 16^2 = 34

These are similar triangles.

∠BAC is congruent to ∠BAD
∠ACB is congruent with ∠ABD (both right angles)

Using ratios:
               AC / AB = AB / (AC + CD)
             AC + CD =  AB² / AC
                       CD = AB² / AC - AC
                       CD = 34² / 16 - 16               
                       CD = 56.25
The answer to this question is 56.

Answer 2

Solution:
Use the Pythagorean theorem:
AB = √30^2 + 16^2 = 34


Since ∠BAC is congruent to ∠BAD
∠ACB is congruent with ∠AB
Then,
 AC / AB = AB / (AC + CD)
 AC + CD =  AB² / AC
CD = AB² / AC - AC
 CD = 34² / 16 - 16               
 CD = 56.25


So the answer is 56