Find the value of x and the value of y.

- ASAPT

Find the value of x and the value of y.

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- ASAPT

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- ASAPT

im not sure im pretty bad at geometry

- ASAPT

ok do you know the answer?

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- anonymous

You can't use the law of cosines unless you know the angle opposite the side you're looking for.

- ASAPT

oh ok do you know the answer?

- ASAPT

ugh why is this so difficult

- ybarrap

Look at the lengths of CB and BA. What is their sum?

- ybarrap

Compare this sum to 48. How is this possible?

- ybarrap

There is only one explanation. Once you see this, the answer will POP.

- ybarrap

Actually, just look at the lengths of CE and BA.

- ybarrap

Sum them and compare to 48. What MUST x be in this case?

- ASAPT

48?

- ybarrap

You know that the lengths of 2 sides of a triangle MUST be greater than the third side, right?

- ASAPT

yea

- ASAPT

so what would that mean my answer is @ybarrap

- ybarrap

forget about that approach

- ASAPT

ok

- ASAPT

its 12 12

- ybarrap

this can't be right, forget that approach too. The reason is that y could be anything and that doesn't make sense.

- ASAPT

no it was I submitted it and it said it was right

- ASAPT

I have more to do if you want to help

- anonymous

|dw:1436331441040:dw|

- ybarrap

I just realized angle D and angle B are equal :(
@surjithayer used similarity - Nice job!

- mathstudent55

You are dealing with two similar triangles.
Since

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- mathstudent55

Now we see how the triangles are similar.
Since x is part of side BC, we need the length of side BC.
From similarity, we get this proportion:
\(\dfrac{CE}{CA} = \dfrac{CD}{BC} \)
\(\dfrac{24}{48} = \dfrac{18}{BC} \)
\(\dfrac{1}{2} = \dfrac{18}{BC} \)
\(BC = 36\)
Since \(BC = 36\), and \(CE = 24\), then \(x = BE = 36 - 24 = 12\)
Now we need y.
\(\dfrac{CE}{CA} = \dfrac{DE}{BA} \)
\(\dfrac{24}{48} = \dfrac{y}{24} \)
\(\dfrac{1}{2} = \dfrac{y}{24} \)
\(y = 12\)

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