How to find dimensions of a field when given length of fencing and area?

[Bernadette]

Hi I really appreciate your help on this.
The question states that I have a field of area 650 square metres and fencing of 110 metres. I must give 3 possible sets of dimensions of the field and the fencing need not cover all four sides of the field.

Thank you so much. Oh I forgot to mention that quadratic algebra and graphing utility must be used.

 

[Deleted member 4993]

Hi I really appreciate your help on this.
The question states that I have a field of area 650 square metres and fencing of 110 metres. I must give 3 possible sets of dimensions of the field and the fencing need not cover all four sides of the field.

Thank you so much. Oh I forgot to mention that quadratic algebra and graphing utility must be used.

What is the shape of the field? Circular, rectangular, elliptic, triangular??

Please share your work with us indicating exactly where you are stuck - so that we may know where to begin to help you.

 

[Bernadette]

Sorry forgot to mention that the field is rectangular and I'm stuck at the part on how to get the dimensions as stated by my previous post. As in how to use quadratic algebra and graphing utility to find the dimensions of the rectangular field.

 

[Bernadette]

Yup i'm sure. But the question is those kind that wants you to be "exposed to real-life algebra questions" therefore quadratic equation must be used and graphing utility (which i have no idea what it is). I'm from Singapore so I'm in sec 2 which is 13-14 years old

 

[Bernadette]

Also the fencing is of the highest importance as in when the sides of the rectangle must add up to 110. And the fencing may not cover all 4 sides of the rectangle. So it is not that easy.

 

[pappus]

Also the fencing is of the highest importance as in when the sides of the rectangle must add up to 110. And the fencing may not cover all 4 sides of the rectangle. So it is not that easy.

OK, let's start from the begin:

Hi I really appreciate your help on this.
The question states that I have a field of area 650 square metres and fencing of 110 metres. I must give 3 possible sets of dimensions of the field and the fencing need not cover all four sides of the field.

Thank you so much. Oh I forgot to mention that quadratic algebra and graphing utility must be used.

1. Let l denote the length of the rectangle and w it's width.

2. As you stated the fencing has to sum up to 110:

\(\displaystyle 2l + 2 w = 110~\implies~l+w=55\)

and consequently \(\displaystyle l = 55-w\)

3. You are supposed to know that the area of a rectangle is calculated by:

\(\displaystyle a = l \cdot w\)

Replace l by 55 - w and you'll get a quadratic function in w:

\(\displaystyle a(w)=l \cdot (55-l)~\implies~ a(w)=-l^2+55l\)

You should see that \(\displaystyle w \in [0,55]\) . Why?

4. To get valid measures of the rectangle you only have to choose for some valid values of w, plug them into a(w) to get the area or plug them into the equation at #2 to get l.

5. To draw the graph of a use any graphics calculator you are allowed to use.

 

[Bernadette]

OK, let's start from the begin:



1. Let l denote the length of the rectangle and w it's width.

2. As you stated the fencing has to sum up to 110:

\(\displaystyle 2l + 2 w = 110~\implies~l+w=55\)

and consequently \(\displaystyle l = 55-w\)

3. You are supposed to know that the area of a rectangle is calculated by:

\(\displaystyle a = l \cdot w\)

Replace l by 55 - w and you'll get a quadratic function in w:

\(\displaystyle a(w)=l \cdot (55-l)~\implies~ a(w)=-l^2+55l\)

You should see that \(\displaystyle w \in [0,55]\) . Why?

4. To get valid measures of the rectangle you only have to choose for some valid values of w, plug them into a(w) to get the area or plug them into the equation at #2 to get l.

5. To draw the graph of a use any graphics calculator you are allowed to use.

Thank you so much

 

[Bernadette]

Oh one more thing... .... if u have the time can u please help me with one more thing please? U see I got two sets of dimensions using quadratic equation but then I can't find the third on. Will the graphing method help and how do u use it? Sorry, I'm only 13 and I got this crazy assignment from my teacher who has not even explained how to draw a curve.

 

[pappus]

Oh one more thing... .... if u have the time can u please help me with one more thing please? U see I got two sets of dimensions <--- I don't get you here
using quadratic equation but then I can't find the third on. Will the graphing method help and how do u use it? Sorry, I'm only 13 and I got this crazy assignment from my teacher who has not even explained how to draw a curve.

I've attached a table where w is running from 5 to 55 in steps of 5.
The dependend values are calculated according to the given equations:

\(\displaystyle l = 55-w\) and

\(\displaystyle a = l \cdot w\)

Maybe this is what you are asking for(?).