Linear inquality help
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Linear inquality help

[From: ] [author: ] [Date: 13-09-28] [Hit: ]
Form a quadratic inequality in x.Please help? How do I do these, could you show working so that I can understand. Thank you :)-If the length is x meters and is 5 m more than the breadth, then the breadth is x - 5 m.......
The specification for a rectangular car park states that the length x metres, is to be 5m more than the breadth. The perimeter of the car park is to be greater than 32m.

Form a linear inquality in x. - how do I do this? I'm confused on the values of x and stuff please help

Secondly, the area of the car park is to be less than 104m^2

Form a quadratic inequality in x.

Please help? How do I do these, could you show working so that I can understand. Thank you :)

-
If the length is x meters and is 5 m more than the breadth, then the breadth is x - 5 m. The perimeter of a rectangle is 2b + 2l where b is the breadth and l is the length, so the inequality that can be set up is:

2x + 2(x - 5) > 32 Since the perimeter has to be GREATER than 32 m. (That's why I put the greater than sign)

The area of a rectangle is (l)(b), so we can just write it as (x)(x - 5) < 104 since the area of the car park is to be LESS than 104.

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Length (x) is 5m longer than the breadth (B) so x = B + 5 or B = x - 5
Perimeter (P) = 2*x + 2*B → P = 2*x + 2*(x - 5)
Since you need an inequality then P > 32m so
2*x + 2*(x - 5) > 32

Area (A) = Length (x) * Breadth (B) → A = x * (x - 5). Since the area < 104m² then x(x-5) < 104m²

-
x^2 5x-104<0
(x 13)(x-8)<0
so
-13
2x 2(x 5)>32
2x>11
x>5.5

-
L = B + 5
P = 2(L+B) = 2(B+5+B) = 32
2B + 5 = 16
B = 11/2 m, L is 10/2 more than B
L = 21/2 m
P = 2(32/2) = 32 m
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