# Math Help - Rectangle formula help please

1. ## Rectangle formula help please

A rectangle is placed under the parabolic arch given by
f(x) = 27 –
3
x2 by using a point (x, y) on the parabola, as shown in the figure.
Write a formula for the function
A(x) that gives the area of the
rectangle as a function of the
x-coordinate of the point chosen.
a.
f(x) = 6(27 – 3x2)
b .
f(x) = 27x – 3x3

c .
f(x) = 54x – 6x3

d . f(x) = 162x – 6x3

Algebra is my weakness. Please help.

2. Here's the pic in a different format

3. Originally Posted by wvmcanelly@cableone.net
A rectangle is placed under the parabolic arch given by
f(x) = 27 –
3
x2 by using a point (x, y) on the parabola, as shown in the figure.
Write a formula for the function
A(x) that gives the area of the
rectangle as a function of the
x-coordinate of the point chosen.
a.
f(x) = 6(27 – 3x2)
b .
f(x) = 27x – 3x3

c .
f(x) = 54x – 6x3

d . f(x) = 162x – 6x3

Algebra is my weakness. Please help.
see the diagram below.

the width of the rectangle is 2x.
the height of the rectangle is y, which is given by y = f(x) = 27 - 3x^2

the area is given by width * height

so A(x) = 2x(27 - 3x^2) = 54x - 6x^3

4. thanks, the explanation is very helpful and easy to understand. I appreciate it.