Chapter 11, Problem 12STP

(a)

To determine

To sketch: a model to represent the problem

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 = $h+3=\left(w-1\right)+3=w+2$

The figure will be:

  

Conclusion:

Therefore, the model was drawn.

(b)

To determine

To write: a polynomial that represents the surface area of the tool chest.

Answer to Problem 12STP

The surface area is $2\left(3x^2+2x-2\right)$ .

Explanation of Solution

Given:

Calculation:

Let x be the width.

Then height will be $\left(x-1\right)$ .

And lenth will be $x-1+3=\left(x+2\right)$ .

So, surface area,

  $\begin{array}{l}2\left(wl+wh+hl\right)\\ =2\left(x\left(x+2\right)+x\left(x-1\right)+\left(x-1\right)\left(x+2\right)\right)\\ =2\left(x^2+2x+x^2-x+x^2+x-2\right)\\ =2\left(3x^2+2x-2\right)\end{array}$

Conclusion:

Therefore, the surface area is $2\left(3x^2+2x-2\right)$ .

(c)

To determine

To find: the dimensions of the of the tool chest.

Answer to Problem 12STP

The width = 3 ft., height=2ft., length=5ft.

Explanation of Solution

Given:

Calculation:

Part C:

Now surface area = 62.

So,

  $\begin{array}{l}2\left(3x^2+2x-2\right)=62\\ 3x^2+2x-2=31\\ 3x^2+2x-33=0\\ 3x^2+11x-9x-33=0\\ x\left(3x+11\right)-3\left(3x+11\right)=0\\ \left(x-3\right)\left(3x+11\right)=0\end{array}$

  $x=3,\frac{-11}{3}$ , 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.