Caseyleia
Badges: 0
Rep:
?
#1
Report Thread starter 6 years ago
#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.
2) form a quadratic inequality
3) by solving your inequalities, determine the value of x
Please help
0
reply
Taelii
Badges: 10
Rep:
?
#2
Report 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.
2) form a quadratic inequality
3) by solving your inequalities, determine the value of x
Please help
What's a breadth ?
0
reply
Caseyleia
Badges: 0
Rep:
?
#3
Report Thread starter 6 years ago
#3
(Original post by Taelii)
What's a breadth ?
the width of the rectangle
0
reply
davros
  • Study Helper
Badges: 16
Rep:
?
#4
Report 6 years ago
#4
(Original post by Taelii)
What's a breadth ?
Have you never heard the phrase "length and breadth"? It's fairly common English
0
reply
Taelii
Badges: 10
Rep:
?
#5
Report 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
0
reply
loperdoper
Badges: 15
Rep:
?
#6
Report 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?
0
reply
Caseyleia
Badges: 0
Rep:
?
#7
Report Thread starter 6 years ago
#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?
0
reply
davros
  • Study Helper
Badges: 16
Rep:
?
#8
Report 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.
0
reply
Caseyleia
Badges: 0
Rep:
?
#9
Report Thread starter 6 years ago
#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.
0
reply
davros
  • Study Helper
Badges: 16
Rep:
?
#10
Report 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.
That looks about right!

Now you need to do a similar thing with the area

Edit: They might expect you to simplify your perimeter inequality btw!
0
reply
Caseyleia
Badges: 0
Rep:
?
#11
Report Thread starter 6 years ago
#11
(Original post by davros)
That looks about right!

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?
0
reply
davros
  • Study Helper
Badges: 16
Rep:
?
#12
Report 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?
0
reply
Caseyleia
Badges: 0
Rep:
?
#13
Report Thread starter 6 years ago
#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?
0
reply
davros
  • Study Helper
Badges: 16
Rep:
?
#14
Report 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!)
0
reply
Caseyleia
Badges: 0
Rep:
?
#15
Report Thread starter 6 years ago
#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?
0
reply
Mr M
Badges: 20
Rep:
?
#16
Report 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.
0
reply
Caseyleia
Badges: 0
Rep:
?
#17
Report Thread starter 6 years ago
#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
reply
Caseyleia
Badges: 0
Rep:
?
#18
Report Thread starter 6 years ago
#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!
0
reply
davros
  • Study Helper
Badges: 16
Rep:
?
#19
Report 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
0
reply
X

Quick Reply

Attached files
Write a reply...
Reply
new posts
Back
to top
Latest
My Feed

See more of what you like on
The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

Personalise

Poll: What factors affect your mental health most right now? Post-lockdown edition

Anxiousness about restrictions easing (21)
6.27%
Uncertainty around my education (36)
10.75%
Uncertainty around my future career prospects (38)
11.34%
Lack of purpose or motivation (47)
14.03%
Lack of support system (eg. teachers, counsellors, delays in care) (17)
5.07%
Impact lockdown had on physical health (14)
4.18%
Social worries (incl. loneliness/making friends) (34)
10.15%
Financial worries (24)
7.16%
Concern about myself or my loves ones getting/having been ill (15)
4.48%
Exposure to negative news/social media (21)
6.27%
Difficulty accessing real life entertainment (9)
2.69%
Lack of confidence in making big life decisions (34)
10.15%
Worry about missed opportunities during the pandemic (25)
7.46%

Watched Threads

View All