Chapter 4.1, Problem 38PPSE

Solution

To Find: The two quantities that required to find area of a rectangle. And state how the graph will be used to solve this problem. Estimate the quadratic function that represents the garden area.

Two quantities that required to find area of a rectangle is length $l$ and breadth $b$ .

The give function's graph is a parabola. So, the vertex of the graph represents the largest area.

Quadratic function: $-w^2+10w$

Given:

Fence measurement $=20m$

Explanation:

Two quantities that required to find area of a rectangle:

Given that fence $=20m$

An area of a rectangle can be calculated by multiplying its length by its width.

If $w$ is the rectangle's width, then the length $l$ can be calculated for the $20m$ fence is:

  $\frac{1}{2}\left(20-2w\right)=10-w$

State how the graph will be used to solve this problem:

In the area function, the graph will resemble a parabola. Using the given amount of fencing,

the vertex of the parabola represents the maximum area that can be produced.

Estimate the quadratic function:

An area of a rectangle is equal to its width times its height:

  $\begin{array}{c}A=w\left(10-w\right)\\ =10w-w^2\end{array}$

Rewrite the equation:

  $-w^2+10w$