
Concept explainers
(a)
To sketch: a model to represent the problem
(a)

Answer to Problem 12STP
Explanation of Solution
Given:
The surface area = 62 square feet
Height should be 1 foot shorter than the width
Length should be 3 feet longer than the height.
Calculation:
Draw the figure in terms of the width.
Width = w
Height = h
Length = h+3=(w−1)+3=w+2
The figure will be:
Conclusion:
Therefore, the model was drawn.
(b)
To write: a polynomial that represents the surface area of the tool chest.
(b)

Answer to Problem 12STP
The surface area is 2(3x2+2x−2) .
Explanation of Solution
Given:
Calculation:
Let x be the width.
Then height will be (x−1) .
And lenth will be x−1+3=(x+2) .
So, surface area,
2(wl+wh+hl)=2(x(x+2)+x(x−1)+(x−1)(x+2))=2(x2+2x+x2−x+x2+x−2)=2(3x2+2x−2)
Conclusion:
Therefore, the surface area is 2(3x2+2x−2) .
(c)
To find: the dimensions of the of the tool chest.
(c)

Answer to Problem 12STP
The width = 3 ft., height=2ft., length=5ft.
Explanation of Solution
Given:
Calculation:
Part C:
Now surface area = 62.
So,
2(3x2+2x−2)=623x2+2x−2=313x2+2x−33=03x2+11x−9x−33=0x(3x+11)−3(3x+11)=0(x−3)(3x+11)=0
x=3,−113 , We take x=3 as length is positive.
So, width = 3 ft., height=2ft., length=5ft.
Conclusion:
Therefore, the width = 3 ft., height=2ft., length=5ft.
Chapter 11 Solutions
Algebra 1
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