As easy as it seems?

Erikina · 2005-07-24 23:14:09

I came across this little problem:

A rectangular room is 3 meters longer than it is wide. If the area of the floor is 88 square meters, what is the length and width of the room?

The problem looked a little like a joke, but just for entertainment - I tried solving it. Half an hour later, I had absolutely no idea where to go. (Obviously after a couple of minutes, I couldn't help noticing the answer, but that's not what I am after).

Could anyone please tell me how to solve this "tricky" problem.

BTW, I've had the problem at "(width * 3) + ( width * width) = 88" but I could get no farther.

Thanks for putting my mind to rest.

mathsyperson · 2005-07-24 23:45:09

This is a quadratic equation.
Calling the short side 'x', you've got x(x+3)=88.
Multiplying out of brackets gives x²+3x=88.
Put it all on one side, because with quadratics that's just what you do: x²+3x-88=0
Factorise it: (x+11)(x-8)=0
There's no short way to factorise things, you just get a knack eventually.
Anyway, as (x+11)(x-8)=0, that means that either x-11 or x-8=0, because anything times 0=0.
So, if x+11=0, rearranging gives x=-11. This would be a valid solution if it was a pure question, but as the question is applied to measurements, negative values are ignored.
This leaves x-8=0, which when rearranged gives x=8, which is the answer.
Your room is 8m wide and 11m long.

Sorry if I've been too complicated or patronising.

MathsIsFun · 2005-07-25 01:03:08

Mathsy has a knack for factorising!

The other way is to use the quadratic formula. You can see that in action here: http://www.mathsisfun.com/forum/viewtopic.php?id=883

EveryoneTookTheGoodNames · 2005-07-25 01:24:04

oh my days - mathsy - you're clever- how old are you?

Erikina · 2005-07-25 09:32:11

Thanks a lot mathsy, I can see what you've done and understand it (but it would be another thing for me to be able to do it).

MathsIsFun, I'll try remember the:
ax² + bx + c = 0
x = (-b ± √(b² - 4ac) / 2a

Thanks a lot guys, it's much appreciated!

Jai Ganesh · 2005-07-25 16:29:36

You may also remember, given the roots of a quadratic equation, the equation can be got thus:-

x² -(Sum of the roots)x + (products of the root) = 0

Math Is Fun Forum

#1 2005-07-24 23:14:09

As easy as it seems?

#2 2005-07-24 23:45:09

Re: As easy as it seems?

#3 2005-07-25 01:03:08

Re: As easy as it seems?

#4 2005-07-25 01:24:04

Re: As easy as it seems?

#5 2005-07-25 09:32:11

Re: As easy as it seems?

#6 2005-07-25 16:29:36

Re: As easy as it seems?

Board footer