Chapter 4.4, Problem 16MCQ

(a)

To determine

To find: The quadratic equation that represents the area of the new slab.

Answer to Problem 16MCQ

The quadratic equation that represents the area of the new slab is $x^2+14x-72=0$ .

Explanation of Solution

Given:

  

The area of the new slab is $120$ square feet.

Length of new rectangle is $\left(x+6\right)$ .

Breadth of new rectangle is $\left(x+8\right)$ .

Area of rectangle is given as:

  $\text{Area}=\left(\text{length}\times breadth\right)$ .

Further simplified for the quadratic equation that represents the area of the new slab is given as:

  $\begin{array}{c}\text{Area}=\left(6+x\right)\left(8+x\right)\\ \text{Area}=x^2+14x+48\\ x^2+14x+48=120\left[\text{given area of new slab is}120\right]\\ x^2+14x-72=0\end{array}$

So the quadratic equation that represents the area of the new slab is $x^2+14x-72=0$ .

(b)

To determine

To find: The dimensions of the new slab.

Answer to Problem 16MCQ

The dimension is $10^{\prime }\times 12^{\prime }$ .

Explanation of Solution

Given:

  

To find the dimension of new slab, first, solve the quadratic equation of the new slab.

  $\begin{array}{c}{x}^2+14x-72=0\\ x^2+18x-4x-72=0\\ \left(x+18\right)\left(x-4\right)=0\\ x=4\left[\text{discard the negative solution}\right]\end{array}$

The length of new slab is $12^{\prime }$ and breadth is $10^{\prime }$ .

Therefore the dimension is $10^{\prime }\times 12^{\prime }$ .