# AS maths

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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.

2) form a quadratic inequality

3) by solving your inequalities, determine the value of x

Please help

1) Form a linear inequality in x.

2) form a quadratic inequality

3) by solving your inequalities, determine the value of x

Please help

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#2

(Original post by

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.

2) form a quadratic inequality

3) by solving your inequalities, determine the value of x

Please help

**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.

2) form a quadratic inequality

3) by solving your inequalities, determine the value of x

Please help

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(Original post by

What's a breadth ?

**Taelii**)What's a breadth ?

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#4

(Original post by

What's a breadth ?

**Taelii**)What's a breadth ?

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#5

(Original post by

Have you never heard the phrase "length and breadth"? It's fairly common English

**davros**)Have you never heard the phrase "length and breadth"? It's fairly common English

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#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?

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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(Original post by

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?

**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?

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#8

(Original post by

Then the length is x and the breadth is x - 5? What do I do now?

**Caseyleia**)Then the length is x and the breadth is x - 5? What do I do now?

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(Original post by

Write down an expression for the perimeter in terms of x. You can use this to form your linear inequality.

**davros**)Write down an expression for the perimeter in terms of x. You can use this to form your linear inequality.

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#10

(Original post by

Would the expression be something along the lines of 4x-10 is greater than 32? Since the perimeter is greater than 32.

**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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#12

(Original post by

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?

**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?

According to your OP the area is

**no less than**104. Is that what the question says?

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(Original post by

Check the wording of the question!

According to your OP the area is

**davros**)Check the wording of the question!

According to your OP the area is

**no less than**104. Is that what the question says?I have as far as x^2 -5x is less than 104, any ideas from here?

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#14

(Original post by

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?

**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?

(If you check the factors of 104 it looks like the quadratic will factorize quite nicely!)

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(Original post by

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!)

**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!)

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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#16

(Original post by

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?

**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?

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(Original post by

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.

**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.

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**davros**)

Have you never heard the phrase "length and breadth"? It's fairly common English

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#19

(Original post by

Thank you very much for all your help davros!

**Caseyleia**)Thank you very much for all your help davros!

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