Pre calculus 12 grade

Question

A rectangle with base x and height y has a perimeter of 175 ft. Express the area A of the rectangle as a function of its base x

A(x)=

Answer 1

2x + 2y = 175 feet

x +y = 175/2 = 87.5 ft.

Area = A = XY = x(87.5-x) = 87.5x -x^2

where x=base length

and y = height of the rectangle

Answer 2

The area of the rectangle is given by A = xy.

We want a function for area in terms of x only. That means we have to replace the "y" with an expression in terms of x. This comes from the given perimeter.

We know that P = 2L + 2W, so:

175 = 2x + 2y

2y = 175 - 2x

y = (1/2)(175 - 2x) [here is the expression for y in terms of x] [replace the y in A = xy with that expression]

A = x (1/2)(175 - 2x)

or

A(x) = (175x)/2 - x²