   Chapter 8.2, Problem 31E Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

Mary Frances has a rectangular garden plot that encloses an area of 48 yd2. If 28 yd of fencing are purchased to enclose the garden, what are the dimensions of the rectangular plot?

To determine

To Find:

The dimensions of the rectangular plot when its’ area and perimeter are provided.

Explanation

Formula Used:

The area A of a rectangle whose base has length b and whose altitude has length h is given by A=bh.

The perimeter of a polygon is the sum of the lengths of all sides of the polygon.

P=2(b+h), where b is length of the base and h is the altitude.

Calculation:

It is given that the rectangular garden plot that encloses an area of 48 yd2and the 28 yd of fencing are purchased to enclose the garden.

Fencing covers the rectangular plot. That gives the perimeter of the rectangular plot.

The area A of a rectangle whose base has length b and whose altitude has length h is given by A=bh=48 yd2 .

The perimeter of a rectangular region is P=2b+h=28 yd,

Consider the equations, bh=48 and 2b+h=28 .

It can be simplified as follows,

h=48b(1)

b+h=14(2)

Substituting the value of 'h' from (1) in (2)

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