Concept explainers
a.
To Make: An expression in terms of width
a.
Answer to Problem 36E
The expression for the perimeter is
Explanation of Solution
Given Information:
The length
Formula:
Perimeter
Calculation: As the length is twice the breadth,
So
Thus
Hence
b.
To Make: An expression in terms of width
b.
Answer to Problem 36E
The expression for the area is
Explanation of Solution
Given Information:
The length
Formula:
Area
Calculation: As the length is twice the breadth,
So
Thus
c.
To Write: Perimeter and area for various values of width in the table.
c.
Answer to Problem 36E
Width (feet) | 1 | 2 | 4 | 8 | 16 |
Perimeter (feet) | 6 | 12 | 24 | 48 | 96 |
Area (square feet) | 2 | 8 | 32 | 128 | 512 |
Explanation of Solution
Given Information:
The values of width
Calculation:
As we found in part (a), part (b)
The perimeter and area are given respectively by
So, for
And for
For
And for
d.
To Describe: How doubling the width affects perimeter and area.
d.
Answer to Problem 36E
On doubling the width, the perimeter becomes double and area becomes four times.
Explanation of Solution
Given Information:
Perimeter
Calculation:
When w changes to
And area becomes
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