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

Answer:

$A=100h-h^2$

Step-by-step 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