Very basic word problem involving use of quad formula

[DeusAbscondus]

A farmer has a rectangular paddock with Perimeter = 50m and Area =130m²
Perimeter =50m
Area of paddock =130m²
The task is find the dimensions of the paddock.

Here is the formula I created to solve this:
l2−25l+130=0
which, when crunched through the Quad Formula, yeilds:
25±105√2
which in turns yields dimensions of paddock to be length≈17.6m & width≈7.4m
My question: how is it that the exponent on 130m² can be whisked away like that and still produce a correct answer?

 

[Sudharaka]

A farmer has a rectangular paddock with Perimeter = 50m and Area =130m²
Perimeter =50m
Area of paddock =130m²
The task is find the dimensions of the paddock.

Here is the formula I created to solve this:
\[l^2−25l+130=0\]
which, when crunched through the Quad Formula, yeilds:
\[25\pm 105\sqrt{2}\]
which in turns yields dimensions of paddock to be length≈17.6m & width≈7.4m
My question: how is it that the exponent on 130m² can be whisked away like that and still produce a correct answer?

Hi DeusAbscondus, :)

Let \(x\) be the width of the paddock and \(y\) be it's length. Note that both of these lengths are in meters. Then,

\[x+y=25m\mbox{ and }xy=130m^2\]

By the second equation we get, \(\displaystyle y=\frac{130}{x}\). Now the units of \(\dfrac{130}{x}\) is meters, since \(130\) is in square meters and \(x\) is a length in meters.

\[\therefore x+\frac{130}{x}=25\]

So all the quantities\(\displaystyle \left(x,\,\frac{130}{x}\mbox{ and }25\right)\) are in meters. Does this answer your question?

Kind Regards,
Sudharaka.

 

[DeusAbscondus]

Hi DeusAbscondus, :)

Let \(x\) be the width of the paddock and \(y\) be it's length. Note that both of these lengths are in meters. Then,

\[x+y=25m\mbox{ and }xy=130m^2\]

By the second equation we get, \(\displaystyle y=\frac{130}{x}\). Now the units of \(\dfrac{130}{x}\) is meters, since \(130\) is in square meters and \(x\) is a length in meters.

\[\therefore x+\frac{130}{x}=25\]

\Would I be right in supplying a step which you seem to have omitted (justifiably considering it too obvious):
namely:
\(\displaystyle y=\frac{130m^2}{xm^1}\)
from which we then get
\(\displaystyle =\frac{130m}{x}\)

 

[Fantini]

Yes. In general, when dealing with units the convention is that you manipulate them algebraically just like everything else, so dividing you subtract powers, multiplying means adding, you can only sum and subtract same units, etc.

 

[DeusAbscondus]

Yes. In general, when dealing with units the convention is that you manipulate them algebraically just like everything else, so dividing you subtract powers, multiplying means adding, you can only sum and subtract same units, etc.

Thanks Fantini.
Would you know of a good supply of pre-calculus level logarithmic worksheets?
(I'm preparing for an exam tomorrow and have run out of exercises with which to practise)

Deus'Abs

 

[Fantini]

Sorry, don't happen to know. I wish you good luck on the test! (Smile)

 

[DeusAbscondus]

I got a reasonable result for the test:

77%

, but what surprised me is that I only had time to answer about 85% of the questions!
I was writing furiously the whole 2 hours and didn't have time to check my answers at the end.

Whereas one other student had 2 toilet breaks and ended up getting 96%

Anyhow, I'm starting from a long way back, not having done maths for 30 years or so, and when i did i was petrified by lack of comprehension of the concepts. I would come from a History or English class with high marks and encouragement from my teachers, and enter the maths classroom with hang-dog expression and eyes cast toward the ground, such was my fear of it.

Now I love it; I just hope it loves me back.
Thanks for the positive wishes and guidance.
Deus' Abs

 

[Fantini]

If you weren't used to the type of the test, don't be so worried. A great score takes in account a lot more than just knowledge, and even that doesn't necessarily weigh so much. Congrats! Keep marching forward! (Clapping)

 

[DeusAbscondus]

If you weren't used to the type of the test, don't be so worried. A great score takes in account a lot more than just knowledge, and even that doesn't necessarily weigh so much. Congrats! Keep marching forward! (Clapping)

Thanks for reminding me to have perspective in this (and indeed in all things)

(Patting myself a little on back because of Fantini's generous encourgement)

Gracie amigo
Deus' Abs