Question

The width of a rectangular sports pitch is x meters, x>0. The length of the pitch is 20 m more than its width. Given that the perimeter of the pitch must be less than 300 m,

a) form a linear inequality in x

Given that the area of the pitch must be greater than 4800 m^2,

b) form a quadratic inequality in x
c) find the set of possible values for x be solving the inequalities.

i got through (a) and (b) but (c) is the one giving me issues,

My answers:
(a) 2x + 2(x+20) <300
simplified...x<65
(b) x(x+2) >4800
simplified...x^2 + 2x >4800

im just not sure how to go about solving c

Answer 1

from the perimeter inequality , you got x<65
now let's find valuse of x from the quadratic equation
we have x^2+2x>4800
x^2+2x-4800>0
when we use quadratic formula the roots are
x=-70.28
x=68.28
so
(x+70.28)(x-68.28)>0
when you solve this you'll get
x<-70.28 or x>68.28
x can't be negative so
only valid condition is x>68.28
we had found x<65 from the perimeter inequality
intersection of these two will give us a null set
so these two can't be satisfied simltaneously

Answer 2

Thank you! that cleared it up :)...i also tried to solve to them quadratically but when the only solution left was 68.28 and the inequality said that it had to be less than 65, i thought i made a mistake and kept redoing the inequalties...thank you again for your time. i appreciate it :)

Answer 3

welcome, glad to help you:)