Can someone help me with with this function word problem?
Creative Landscaping has 60yd of fencing with which to enclose a rectangular flower garden. If the garden is x yards long, express the garden’s area as a function of the length.
I know the answer is
A(x)=30x-x^2
But I have no idea how to get it.
Can someone explain it?
Details:
- let the garden be a x * y area
you know that x+y+x+y = 60yd =>
2x+2y=60=>
2y=60-2x=>
y=30-x
the area is A = x*y , replace y:
A(x)=x*(30-x)=>
A(x)=30x-x^2
EDIT: this is what the garden look like:
..._____x_____
...|..................|
y |..................| y
...|__________|
.............x
- The length is x. There are two sides of length x so that uses up 2x yards of fencing.
That leaves 60-2x yards of fencing. So the width of the rectangle is ½(60-2x) = 30-x yards. We find the area by multiplying the length by the width: x(30-x). Multiply out the brackets to get 30x-x².
I hope this helps.