The ones I know are know are correct but no well understood:

a) 1:1 because both triangles have the same base? So 16:16 = 1:1 right?
b) same method as ^
d) 9:16 because using the similar triangles area ratio formula. The method of similar trianges i used was AA because of the parallel lines right?

The ones I don't understand at all but I know the answers. I'm all confused:

c) The answer is 1:1. I think you can assume that the height of both triangles are the same? How can it be 1:1 if there are no other measurements of the triangles?
e) The answer is 3:4. I figured maybe you do simplfy 12/16 to get 3:4 but I have no clue why because the the triangles that the question is asking for doesn't have 12 or 16?

2. Originally Posted by AirForceOne
...
The ones I don't understand at all but I know the answers. I'm all confused:
c) The answer is 1:1. I think you can assume that the height of both triangles are the same? How can it be 1:1 if there are no other measurements of the triangles?
e) The answer is 3:4. I figured maybe you do simplfy 12/16 to get 3:4 but I have no clue why because the the triangles that the question is asking for doesn't have 12 or 16?
Hello,

let H be the height of the trapezoid and h the height of triangle(ZYP) (I#ve attached a diagram to demonstrate, what I'll calculate).
Then you get the proportion:
$\displaystyle \frac{h}{16}=\frac{H-h}{12}$. Solve for h and you'llget h = 4/7*H.

to e.: You get the area of triangle(XPY) by:
$\displaystyle A_{\Delta XPY}=A_{\Delta WXY}-A_{\Delta WXP}$

$\displaystyle \frac{1}{2} \cdot 12 \cdot H-\frac{1}{2} \cdot 12 \cdot \frac{3}{7} \cdot H=\frac{1}{2} \cdot 12 \cdot H \cdot \frac{4}{7}$
That means:
$\displaystyle \frac{A_{\Delta XPY}}{A_{\Delta WXP}}=\frac{\frac{1}{2} \cdot 12 \cdot H \cdot \frac{4}{7}}{\frac{1}{2} \cdot 12 \cdot \frac{3}{7} \cdot H}=\frac{4}{3}$

to d.: As I've shown above you can calculate the areas of the triangles in question by calculating the differences of two triangles.
Unfortunately I'm a little bit in a hurry to complete the problem, but I'm certain that you now know how to handle the problem.

Greetings and Happy Easter to you.

EB

3. Originally Posted by AirForceOne
...
The ones I don't understand at all but I know the answers. I'm all confused:
c) The answer is 1:1. I think you can assume that the height of both triangles are the same? How can it be 1:1 if there are no other measurements of the triangles?
...
Hello,

to c.: as you've demonstrated:
$\displaystyle A_{\Delta ZYW}=A_{\Delta ZYX}$ (same base, same height). Thus

$\displaystyle A_{\Delta ZYW}-A_{\Delta ZYP}=A_{\Delta ZYX}-A_{\Delta ZYP}$

$\displaystyle A_{\Delta WZP}=A_{\Delta XYP}$. Thus the ratio is 1:1.

Greetings

EB