Question

HELP ASAP How do I find the answer to this

Answer 1

Since triangle ABD and triangle BCD are similar traingles, we can establish a proportion between the lengths of corresponding sides:
$\frac{CD}{BD} = \frac{BD}{AD}$

Notice that we know for our problem that $BD=h$. Also, we can find the length of AD by subtracting CD from AC:
$AD=AC-CD$
$AD=25-16$
$AD=9$

Now we can replace the values in our proportion:
$\frac{CD}{BD} = \frac{BD}{AD}$
$\frac{16}{h} = \frac{h}{9}$
Solving for $h$:
$h^2=(16)(9)$
$h^2=144$
$h= \sqrt{144}$
$h=12$

We can conclude that the correct answer is: B. 12

Answer 2

AC=25

Triangle BCD:
BD=h
CD=16

Triangle ABD:
BD=h
AD=AC-CD=25-16→AD=9

Suppose <CBD is x and the <ABD is y
x+y=90°

The <BCD must be equal to y; and the <BAD must be equal to x, then the triangles ABD and BCD are similars, because they have two congruent angles (x and y), so theirs sides must be proportionals:

Opposite to angle x / opposite to angle y

Triangle ABD         Triangle BCD
    BD / AD          =      CD / BD

Replacing values:
h/9=16/h

Solving for h. Cross multiplication:
(h)(h)=(9)(16)
h^(1+1)=144
h^2=144
sqrt(h^2)=sqrt(144)
h=12

Answer: The value of h in the figure is 12