Geometry Help

I can't figure out this problem!

An airplane has a wingspan of (x^2+1) ft and a length of (x^2-9) ft. A scale model of this plane has a wingspan of (x+3) ft and a length of (x+1) ft. Based on this information, use a proportion to find the wingspan of the actual airplane.

It won't work because I can't get the proportion right.

I think the proportion is (x^2+1)/(x+3) = (x^2-9)/(x+1). But they don't equal eachother. >< Heelpp!

By setting the two sides equal, its not a question if they're equal or not, but for which values of x they are equal. Now, you are correct in your representation of the ratios as fractions, what remains is to expand them and form an algebraic equation in terms of x. By solving the equation, you will find a value of x, which will allow you to work out the dimensions of the airplane.

Well, when using that proportion, I get 2X^2-10X-28.

So then, I attempt to factor it. I use the slide and divide method my teacher taught me. So that makes it X^2-10X-56=0.

Now attempting to factor that, I get that it should look like ( + )( - ), no? Well, the numbers I come up with are 14*4=56 and 14-4=10. That works out. So now it looks like (x+4) (x-14). Now since I used slide and divide I have to divide the numbers by 2 (the number I multiplied 28 by in the begining) giving me (x+2) (x-7). But my teacher says that one of the numbers should ALWAYS be a fraction. Thats where I get confused.

I'm unfamiliar with this slide-and-divide method, but you could just take 2X^2-10X-28=0 and divide everything by 2, leading to X^2-5X-14=0, which again gives you (x+2)(x-7). But that's the answer, I don't see where fractions are needed. You just now use the brackets to find a value for x, try it.

There's supposed to be a fraction though...

I guess I could try. I hope it works.

Originally Posted by Drewey

I can't figure out this problem!

An airplane has a wingspan of (x^2+1) ft and a length of (x^2-9) ft. A scale model of this plane has a wingspan of (x+3) ft and a length of (x+1) ft. Based on this information, use a proportion to find the wingspan of the actual airplane.

It won't work because I can't get the proportion right.

I think the proportion is (x^2+1)/(x+3) = (x^2-9)/(x+1). But they don't equal eachother. >< Heelpp!

First it is not "(x^2+1)/(x+3) = (x^2-9)/(x+1)", because the scale is a fraction of the original you should have it "(x+3)/(x^2+1) = (x+1)/(x^2-9)".

Then you would cross multiply (x^2+1) by (x+1) and (x^2-9) by (x+3).

You end up with (x^2+1)(x+1) = (x^2-9)(x+3), which you would factor.

x^3 + x^2 + x + 1 = x^3 + 3x^2 - 9x - 27

2x^2 - 10x - 28 = 0

factor, (x+2)(x-7) = 0

so your solutions are -2 and 7, I checked both of them and they both work. I don't know why your teacher told you it should be a fraction. I have to agree with Andúrhil. Sorry I'm in Pre-Calculus and I've never been told that one should be a fraction, don't know where that came from.

No... meaning one should divide perfectly, leaving you with something like (x+2)(2x-7). I dunno if that even works but thats what I meant. XP

Originally Posted by Drewey

No... meaning one should divide perfectly, leaving you with something like (x+2)(2x-7). I dunno if that even works but thats what I meant. XP

Umm... that makes no sense. When solving a quadratic and using the zero product property to find your solutions you get two polynomials, like I left above (x+2)(x-7) which are set equal to 0. Then you solve for each one,

x+2 = 0 and x-7 = 0

When you solve you get the solutions of -2 and 7

Now take those two numbers, one at a time, and plug them into all the x's, when you do that the fractions should be the same on both sides. When you plug in 7 you get 1/5 = 1/5 and the same happens for -2. Since 1/5 = 1/5 is true the solutions work, so the correct answers are -2 and 7.

Alright... I guess.

I'll have to ask my teacher, though. Maybe I misunderstood. =/

Originally Posted by Drewey

Alright... I guess.

I'll have to ask my teacher, though. Maybe I misunderstood. =/

Yes it seems that what he said was misunderstood, seems logical. Don't worry I don't always pay attention, I just read what the book says and I know sometimes what I think I hear my teacher say is quite different that what he actually said. Ask him to make sure, but I don't ever recall being told something along those lines, also it might be a good idea to check the book. You might find what your teacher was explaining there.

He said the slide and divide method isn't in the book, but is very easy.

I hope it's a little misunderstanding. >< I don't trust math books... sometimes they're so hard to understand.

It was done right before, but it should be noted that there isn't one specific set of proportions that work. As long as each proportion or the numerators/denominators of both fractions are comparing similar things, such as wing length, then it works. For any 4 values, there are 4 different proportions possible. In this instance you could use and of:

(x^2+1)/(x+3) = (x^2-9)/(x+1) (planewing/modelwing = planelength/modellength)
(x+3)/(x^2+1) = (x+1)/(x^2-9) (modelwing/planewing = modellength/planelength)
(x+3)/(x+1) = (x^2+1)/(x^2-9) (modelwing/modellength = planewing/planelength)
(x+1)/(x+3) = (x^2-9)/(x^2+1) (modellength/modelwing = planelength/planewing)

They all give the same equation when cross multiplied.