a farmer has 120m of fencing. by using an existing wall, h decides to make a rectangular pen by adding 3 sides, with 2 sides equal to x m as shown in the diagram. show that the area enclosed, A m^2, is given by A=x(120-2x).
complete the square on the expression for A and hence find the greatest value of A and the value of x for which this occurs
2007-09-24 04:50:02 · 2 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
A = -2 (x^2 - 60x)
= -2 (x^2 - 60x + 30^2 - 30^2)
= -2 (x - 30)^2 + 2*30^2
So max A = 1800 when (x-30)=0 => x=30
2007-09-24 05:04:39 · answer #1 · answered by simpsons_simp 2 · 0⤊ 0⤋
A=x(120-2x)
A= (120x - 2x^2)
Greatest value for A is 120 - 4x
It's when x= 30 A = 1800 square meters
The pen is 30m by 60m
2007-09-24 11:59:12 · answer #2 · answered by Will 4 · 0⤊ 0⤋