Chapter 7.2, Problem 11P

To determine

Tofind:The value of x in the given figure.

Answer to Problem 11P

The value of x is 1.3899 m.

Explanation of Solution

Given:

The total surface area of the rectangular solid = 36 m².

The given figure is:

Calculation:

The total surface area of the rectangular solid is given by

  $\begin{array}{c}SA=2\left(\left(2x\times x\right)+\left(x\times \left(x+2\right)\right)+\left(2x\times \left(x+2\right)\right)\right)\\ =2\left(2x^2+x^2+2x+2x^2+4x\right)\\ =10x^2+12x\end{array}$

Substitute 36 for SA .

  $\begin{array}{l}36=10x^2+12x\\ 10x^2+12x-36=0\end{array}$

The solution of the given equation is obtained by using the quadratic formula.

For a quadratic equation in the form of $a{x}^2+bx+c=0$ , the solution of this equation is given by

  $x_{1,2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

Comparing the given equation with the standard quadratic equation, the coefficients are:

  $\begin{array}{l}a=10\\ b=12\\ c=-36\end{array}$

Substituting these in the formula for the roots.

First take the positive sign.

  $\begin{array}{c}{x}_1=\frac{-\left(12\right)\pm \sqrt{{\left(12\right)}^2-4\times 10\times \left(-36\right)}}{2\times 10}\\ =\frac{-12\pm \sqrt{144+1440}}{20}\\ =\frac{-12\pm 39.799}{20}\\ =1.3899,-2.5899\end{array}$

The dimension cannot be negative.

The value of x is 1.3899 m.

Therefore, the value of x is 1.3899 m.