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**Erikina****Member**- Registered: 2005-07-24
- Posts: 5

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.

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**mathsyperson****Moderator**- Registered: 2005-06-22
- Posts: 4,900

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.

Why did the vector cross the road?

It wanted to be normal.

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,631

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

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

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**EveryoneTookTheGoodNames****Member**- Registered: 2005-07-19
- Posts: 155

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

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**Erikina****Member**- Registered: 2005-07-24
- Posts: 5

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!

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 22,059

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

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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