Need Help with Geometry and Ratio!!!!

- anonymous

Need Help with Geometry and Ratio!!!!

- chestercat

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- anonymous

In the diagram, AX = 10, XB=5, AY=4 and YC=8. What is the ratio of the area of AXY to the area of ABC? Express your answer as a common fraction.

- anonymous

|dw:1327715430695:dw|

- Directrix

Are the triangles given to be similar? If so, what is the correspondence of vertices? Would you check to determine if the diagram is correctly labeled? Thanks.

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## More answers

- anonymous

The diagram (seems) not correct.

- Directrix

I agree. I think that the SAS Similarity Theorem is needed for solution but the given data doesn't satisfy the theorem's hypothesis.
Triangles are similar if two sides in one triangle are in the same proportion to the corresponding sides in the other, and the included angles are equal.

- anonymous

this is all the given information

- anonymous

I could draw the diagram again to clarify.

- anonymous

|dw:1327717724546:dw|

- Directrix

Are both the black segments of length h? It seems that they would differ in length. And, are the segments labeled h perpendicular to segment AB?

- anonymous

How come the black segments be equal in length? or am I misunderstanding ?!

- anonymous

yeah sorry, they don't have the same length and i believe they are perpendicular. That was the hint from my teacher.

- anonymous

|dw:1327720461436:dw|

- anonymous

are you sure that this are the only given?

- anonymous

yes

- anonymous

I think it has something to do with ratio

- anonymous

i have here only assumptions. .

- anonymous

ok

- anonymous

the area of ACB-Ayx= area of CyxB
the area of ACB-CyxB= area of Ayx

- anonymous

Yes, but how do I find the area?

- anonymous

this is what I've got
4/12 = p/h
4h/12=p
|dw:1327722363321:dw|

- anonymous

but i am not sure how to find ABC.

- anonymous

your problem is ABC?
find area of ACB:
sinA=h/(8+4) therefor h=12sinA
area = 1/2bh
= 1/2(10+5)(12sinA) ; substitute the value of h in the formula
= 1/2(15)(12sinA)
therefor: the area of ACB is 90sinA

- anonymous

Can you clarify sinA?

- anonymous

no it,s not (8+4) for h, it's 10+5 , and (10+5) is 8+4, but anyway the answer is still 90 sinA

- anonymous

sin A will be find if there's a given measure for the angle. .

- anonymous

ok

- anonymous

thanks

- anonymous

you're welcome. .

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