having trouble with geometry problem w/ ratios

[lahzika]

Good afternoon!
I'm having trouble getting out of here. I only know the sides of triangles/trapezoids, but I don't even know the lengths of the bases or heights. This is the only information that is given.
(also sorry for poor english.)

 

[blamocur]

I agree with you that there is not enough information to get to the answer. Maybe the solution is to compute the area relative to the total area of the ABC triangle ?

 

[lookagain]

I agree with you that there is not enough information to get to the answer.

I am trying to edit to this.

There is enough information to find the requested ratio.

Because of proportions in the triangles, we may let the lengths of DE, FG, and BC
be 2x, 5x, and 6x, respectively. These are lengths of bases of trapezoids.

Let the heights of Trapezoids DEGF and FGCB be 3y and y, respectively.

Use the formula for the area of a trapezoid: (1/2)(height)(sum of bases).

Simplify down to a number.

 

[Otis]

find the requested ratio.

I don't see that they've requested those areas as ratios, but that's probably what they're thinking.

I set the area of triangle ABC to 1 and stated the requested areas as percentages of the whole.

[imath]\;[/imath]

 

[Dr.Peterson]

I don't see that they've requested those areas as ratios, but that's probably what they're thinking.

I think that's what the colon means:



Everything in the problem is ratios.

I found the ratios of sides of the three similar triangles (ADE, AFG, ABC), from that found the ratios of their areas, and did some subtracting to find the ratio of the trapezoids. Working entirely with ratios (well, actually I thought in terms of "parts") makes it easy -- but perhaps harder to explain to a newcomer to these ideas. Ultimately I'd like to see the OP's attempt so we can suggest improvements.

@lahzika, have you learned that the ratio of areas of similar figures is the square of the ratio of the sides?

 

[blamocur]

I think that's what the colon means:

View attachment 32324

Everything in the problem is ratios.

I found the ratios of sides of the three similar triangles (ADE, AFG, ABC), from that found the ratios of their areas, and did some subtracting to find the ratio of the trapezoids. Working entirely with ratios (well, actually I thought in terms of "parts") makes it easy -- but perhaps harder to explain to a newcomer to these ideas. Ultimately I'd like to see the OP's attempt so we can suggest improvements.

@lahzika, have you learned that the ratio of areas of similar figures is the square of the ratio of the sides?

Good catch!

 

[Otis]

Thanks, Doc. I'd completely read over that last colon. Maybe my mind thought it was a semicolon? (Yeah, that's the ticket...)

?

[imath]\;[/imath]

 

[topsquark]

Thanks, Doc. I'd completely read over that last colon. Maybe my mind thought it was a semicolon? (Yeah, that's the ticket...)

?

[imath]\;[/imath]

We don't have much space in the corner but you can sit on my lap if you like.

-Dan

 

[Dr.Peterson]

Thanks, Doc. I'd completely read over that last colon. Maybe my mind thought it was a semicolon? (Yeah, that's the ticket...)

?

[imath]\;[/imath]

Actually, I had considered adding a comment about the unfortunate wording of the problem, which obscures the colon.

I assume the line is intended to be read as "Find the ratio of the area of DEGF to the area of FGCB"; but when you read it, you get too deep into "find the area of DEGF ..." to back out and insert "the ratio of" into what your mind has already thought it understood. If it were, say, "Find area(DEGF) : area(FGCB)" it would be easier to read.

(The darkness of the image also literally obscures the colon.)

So I suggest going into a relatively well-lit corner.

 

[Steven G]

We don't have much space in the corner but you can sit on my lap if you like.

-Dan

I don't think we allow such things in this forum.