AS maths

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 :frown:

Reply 1

Taelii

Original post by Caseyleia

What's a breadth :smile:

Reply 2

Caseyleia

Original post by Taelii

What's a breadth :smile:

the width of the rectangle

Reply 3

davros

Original post by Taelii

What's a breadth :smile:

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

Reply 4

Taelii

Original post by davros

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

I just call it the width :smile:

Reply 5

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?

(edited 9 years ago)

Reply 6

Caseyleia

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?

Reply 7

davros

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.

Reply 8

Caseyleia

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.

Reply 9

davros

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.

That looks about right!

Now you need to do a similar thing with the area :smile:

Edit: They might expect you to simplify your perimeter inequality btw!

(edited 9 years ago)

Reply 10

Caseyleia

Original post by davros

That looks about right!

Now you need to do a similar thing with the area :smile:

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?

Reply 11

davros

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?

Reply 12

Caseyleia

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?

Reply 13

davros

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!)

Reply 14

Caseyleia

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?