# AS maths

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#1
The specification for a rectangular car park states that the length x metres is to be 5 metres greater than the breadth. The perimeter of the car park is to be greater than 32 metres. The area is to be no less than 104 metres squared.
1) Form a linear inequality in x.
3) by solving your inequalities, determine the value of x
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6 years ago
#2
(Original post by Caseyleia)
The specification for a rectangular car park states that the length x metres is to be 5 metres greater than the breadth. The perimeter of the car park is to be greater than 32 metres. The area is to be no less than 104 metres squared.
1) Form a linear inequality in x.
3) by solving your inequalities, determine the value of x
0
#3
(Original post by Taelii)
the width of the rectangle
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6 years ago
#4
(Original post by Taelii)
Have you never heard the phrase "length and breadth"? It's fairly common English
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6 years ago
#5
(Original post by davros)
Have you never heard the phrase "length and breadth"? It's fairly common English
I just call it the width
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6 years ago
#6
If your length is meant to be 5 metres longer than the breadth, then you have two unknowns.

If your length is "breadth plus five metres", and the length is "x", can you see where to go from here?
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#7
(Original post by loperdoper)
If your length is meant to be 5 metres longer than the breadth, then you have two unknowns.

If your length is "breadth plus five metres", and the length is "x", can you see where to go from here?
Then the length is x and the breadth is x - 5? What do I do now?
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6 years ago
#8
(Original post by Caseyleia)
Then the length is x and the breadth is x - 5? What do I do now?
Write down an expression for the perimeter in terms of x. You can use this to form your linear inequality.
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#9
(Original post by davros)
Write down an expression for the perimeter in terms of x. You can use this to form your linear inequality.
Would the expression be something along the lines of 4x-10 is greater than 32? Since the perimeter is greater than 32.
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6 years ago
#10
(Original post by Caseyleia)
Would the expression be something along the lines of 4x-10 is greater than 32? Since the perimeter is greater than 32.

Now you need to do a similar thing with the area

Edit: They might expect you to simplify your perimeter inequality btw!
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#11
(Original post by davros)

Now you need to do a similar thing with the area
For the area, I would do x multiplied by x-5 which would give me x^2 - 5x. Therefore would the inequality be x^2 -5x is less than 104?
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6 years ago
#12
(Original post by Caseyleia)
For the area, I would do x multiplied by x-5 which would give me x^2 - 5x. Therefore would the inequality be x^2 -5x is less than 104?
Check the wording of the question!

According to your OP the area is no less than 104. Is that what the question says?
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#13
(Original post by davros)
Check the wording of the question!

According to your OP the area is no less than 104. Is that what the question says?
Sorry the written question says less then! Thank you for spotting my mistake!
I have as far as x^2 -5x is less than 104, any ideas from here?
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6 years ago
#14
(Original post by Caseyleia)
Sorry the written question says less then! Thank you for spotting my mistake!
I have as far as x^2 -5x is less than 104, any ideas from here?
Rearrange as a standard quadratic i.e. something < 0 then find the range(s) of values of x that work.

(If you check the factors of 104 it looks like the quadratic will factorize quite nicely!)
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#15
(Original post by davros)
Rearrange as a standard quadratic i.e. something < 0 then find the range(s) of values of x that work.

(If you check the factors of 104 it looks like the quadratic will factorize quite nicely!)
All completed! Thank you!
I have one final question.
The first question gave me an answer of x>10.5, and the second question gave me -8<x<13.
However, the answer to the final question ( possible values of x) is 10.5<x<13. What happened to the -8 I got from factorising the second question? Is it because the value is a negative?
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6 years ago
#16
(Original post by Caseyleia)
All completed! Thank you!
I have one final question.
The first question gave me an answer of x>10.5, and the second question gave me -8<x<13.
However, the answer to the final question ( possible values of x) is 10.5<x<13. What happened to the -8 I got from factorising the second question? Is it because the value is a negative?
Think about the values of x that satisfy BOTH inequalities. Obviously it isn't possible to have a negative length anyway so that is relevant.
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#17
(Original post by Mr M)
Think about the values of x that satisfy BOTH inequalities. Obviously it isn't possible to have a negative length anyway so that is relevant.
Fantastic! I completely understand! Thank you! Thank the stars I only have one question left on the homework sheet! Thank you again!
1
#18
(Original post by davros)
Have you never heard the phrase "length and breadth"? It's fairly common English
Thank you very much for all your help davros!
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6 years ago
#19
(Original post by Caseyleia)
Thank you very much for all your help davros!
np - glad you got it sorted in the end
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