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Chapter 9: Problem 79

Describe the difference between the following problems: How much fencing is needed to enclose a garden? How much fertilizer is needed for the garden?

Short Answer

Expert verified
The difference between the two problems lies in the type of calculation needed. The fencing question is about finding the perimeter of the garden, which implies measuring the outline length of the garden. On the other hand, the fertilizer question is about finding the area of the garden as it pertains to how much fertilizer will be spread out over the entire garden.

Step by step solution

01

Identifying the type of problem

First, identify the difference between the two problems. The first problem is a geometry problem as it is asking to calculate the amount of fencing needed, which directly correlates with the perimeter of the garden. The second problem is more of agronomy or gardening area related problem since it is asking about the amount of fertilizer needed which would be dependent on the area of the garden.
02

Solving Perimeter Problems

To solve the problem of how much fencing is needed to enclose a garden, it is necessary to calculate the length of the garden's outline, also known as the perimeter. In case of a rectangular garden, the formula would be \(P=2L+2W\), where \(L\) is the length and \(W\) is the width. You measure the length and the width of the garden in the same units as the fencing you plan to buy (usually meters), plug those values into the formula, and that鈥檚 how much fencing you would need.
03

Solving Fertilizer Problems

On the other hand, calculating how much fertilizer is needed is determined by the area of the garden. Fertilizer should typically be spread uniformly across the entire garden. First, you鈥檇 need to calculate the area of the garden. For a rectangular garden, \(A=L*W\), where \(A\) is the area, \(L\) is the length, and \(W\) is the width. Next, the package of fertilizer often states how much you have to use per unit of area (square meters in many cases). Multiply this rate with the calculated area of the garden to find out how much fertilizer is needed.

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