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HELP ASAP How do I find the answer to this

HELP ASAP How do I find the answer to this-example-1
User Victrnava
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2 Answers

5 votes
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


HELP ASAP How do I find the answer to this-example-1
User FlyingTeller
by
8.6k points
7 votes
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
User Gladed
by
9.0k points

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