Question

HELP ASAP How do I find the answer to this

Answer 1

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

Answer 2

Since triangle ABD and triangle BCD are similar traingles, we can establish a proportion between the lengths of corresponding sides:

`(CD)/(BD) = (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:

`(CD)/(BD) = (BD)/(AD)`

`(16)/(h) = (h)/(9)`
Solving for
`h`:

`h^2=(16)(9)`

`h^2=144`

`h= √(144)`

`h=12`

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