Help on a geometry problem
Oct 25, 2008 at 10:40 PM Thread Starter

#### ShinyFalcon

##### 500+ Head-Fier
My sister needs some help on this particular problem. I have forgotten all of my geometry, so I can't be of any help for her (shame on me ). The answer supposedly is x = 6.

Picture attached. I'm assuming that the equations refer to the length of the line, not the angles. x = 6 doesn't make sense if they were angles. Oct 25, 2008 at 11:00 PM

#### jazzychu

##### Head-Fier
9/(x-3)=(x+6)/4 ---> x=6

Get her to open (and study) the textbook.......

Oct 25, 2008 at 11:02 PM

#### ptl

##### New Head-Fier
This is probably all wrong, but:

The parallel lines indicate that the trapezium on the right is just a scaled up version of the one on the left. So the ratio of the sides should be the same.

Therefore:
4/(x-3) = (x+6)/9

Which becomes:
36 = (x+6)(x-3)
36 = x² + 3x -18
0 = x² +3x - 54
0 = (x+9)(x-6)

Giving x = 6 (x can't be -9 for obvious reasons)

Oct 25, 2008 at 11:12 PM

#### ShinyFalcon

##### 500+ Head-Fier
My sister just entered high school, and she does have a learning disability, so be a bit nice to her... it isn't obvious to me too as I never did well in geometry.

I was looking for some reasoning like step by step proofs, but I don't know what I'm supposed to do since she only gave me the picture and the solution.

Edit: Thanks ptl and jazzychu, I'll pass that to her.

Oct 25, 2008 at 11:41 PM

#### AlanY

##### 1000+ Head-Fier
Quote:

 Originally Posted by ShinyFalcon /img/forum/go_quote.gif I was looking for some reasoning like step by step proofs, but I don't know what I'm supposed to do since she only gave me the picture and the solution.

The concept she needs to understand to do this problem is geometric similarity. She might only have seen the concept of "similarity of triangles" before. It's worth reviewing that if she's not familiar with it, since most geometry problems of this type involve similarity of triangles.

It's possible to solve this problem just using the concept of similarity of triangles, by introducing variables A and B to represent the distance between the first pair of parallel lines and the second pair of parallel lines respectively. Using the concept of similarity of triangles for the top line, we get (x-3)/a = 9/b. Then using it for the bottom line, we get 4/a = (x+6)/b. Rearranging these two pairs of equations, we get b/a = 9/(x-3) and b/a = (x+6)/4. Then equate the two pairs, getting rid of the b/a, giving us 9/(x-3)=(x+6)/4, and solve.

After she understands that, it's worth looking at the problem from a more general concept of geometric similarity. Here the trapezoid on the left is similar to the trapezoid on the right, so we can just write 4/(x-3) = (x+6)/9 and solve.

It's worth solving the problem in both these ways because it will help her understand that you can solve problems in different ways and it will also help her understand the concept of similarity if she sees it in two different ways.

Oct 25, 2008 at 11:48 PM

#### myinitialsaredac

##### 1000+ Head-Fier
I arrived too late on the scene to be cool. Good work gentlemen.

Dave

Oct 26, 2008 at 12:21 AM

#### jazzychu

##### Head-Fier
The reason I provided the answer was I noticed you are also in Houston. Now that I know your sister is in 9th grade, I happen to have one in the family in 9th grade -- my daughter.

Give your sister a big credit for wanting to do the homework, especially on Saturday, or make it a pretty weathered Saturday. Kudo to yourself too for helping her.