Concept explainers
(a)
To find: The polynomial that represents the area of Kelly’s plot.
(a)
Answer to Problem 1MP
Explanation of Solution
Given Information:
Formula Used:
Area of a rectangle of length l and width b is lb
Calculation:
Length of Kelly’s plot, l =
Width of Kelly’s plot, b =
Length and width of Kelly’s plot are binomials (since it contains two terms)
Therefore the area is the product of two binomials.
Area of Kelly’s plot,
(b)
To find: The polynomial that represents the area of Roberto’s plot.
(b)
Answer to Problem 1MP
Explanation of Solution
Given Information:
Formula Used:
Area of a rectangle of length l and width b is lb
Calculation:
Length of Roberto’s plot, l =
Width of Roberto’s plot, b =
Length and width of Roberto’s plot are binomials (since it contains two terms)
Therefore the area is the product of two binomials.
Area of Roberto’s plot,
(c)
To check: the products found in (a) and (b) are correct by applying a value for x.
(c)
Explanation of Solution
Given Information:
Kelly’s plot Length =
Breadth=
Roberto’s plot Length =
Breadth =
Proof:
Let’s assume that
For Kelly’s plot Length = 7
Breadth= 3
Area =
Now let’s compute the area using
Which is same as
Roberto’s plot Length = 7
Breadth= 4
Area =
Now let’s compute the area using
Which is same as
∴The polynomials found in (a) and (b) are correct.
(d)
To check: whether the area of Roberto’s plot is greater than Kelly’s plot.
(d)
Answer to Problem 1MP
Area of Roberto’s plot is greater than that of Kelly’s plot.
Explanation of Solution
Given Information:
The area of Roberto’s plot is
The area of Kelly’s plot is
Proof:
From part (c)
For
The area of Roberto’s plot = 28 sq.ft
The area of Kelly’s plot = 21 sq.ft
That is, for
Area of Roberto’s plot is greater than that of Kelly’s plot……. (1)
Since the area is true for all values of x, (1) is true for all values of x
Chapter 8 Solutions
High School Math 2015 Common Core Algebra 1 Student Edition Grade 8/9
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