Question

a world class barrel racing champion wants to build a custom practice area. She wants to keep a perimeter of 200ft. Express the Area A(l) for a rectangle with this perimeter.

Answer 1

`A=100h-h^2`

Explanation:

Area and Perimeter of a Rectangle

A rectangle is a four-sided shape where each pair of opposite sides have the same length and all the internal angles are 90°. The area of a rectangle with sides b and h is

`A=b.h`

The perimeter is the sum of all 4 sides

`P=2b+2h`

We know the perimeter of the rectangle is 200 feet, thus

`2b+2h=200`

Or, equivalently

`b+h=100`

`b=100-h`

Replacing b in the formula for the area, we have

`A=(100-h).h`

`\boxed{A=100h-h^2}`

For example, if h=30, the area is

A=100*30-30^2=3000-900=2100