Chapter 14.8, Problem 3GP

(a)

To determine

To calculate: The dimension of the platform in terms of $y$ .

Answer to Problem 3GP

The dimension of the platform are $y-3=0\text{and}y+1=0$ .

Explanation of Solution

Given Information:

  $\text{Area}\text{of}\text{the}\text{platform}=y^2-2y-3\text{square}\text{unit}$ .

Calculation:

The given area of the platform is $y^2-2y-3$ square unit.

Find the factors of the expression $y^2-2y-3$ .

Split $-2y$ into two parts such that their product is equal to the product of $y^2$ and $-3$ .

  $\begin{array}{c}{y}^2-2y-3=y^2-3y+y-3\\ =y\left(y-3\right)+1\left(x-3\right)\\ =\left(y+1\right)\left(y-3\right)\end{array}$

Hence, the dimension of the platformare $y-3=0\text{and}y+1=0$ .

(b)

To determine

To calculate: The area of the platform when $y=8$ .

Answer to Problem 3GP

The area of the platform is 45 square unit.

Explanation of Solution

Given Information:

  $\text{Area}\text{of}\text{the}\text{platform}=y^2-2y-3\text{square}\text{unit}$

  $y=8$

Calculation:

The given area of the platform is $y^2-2y-3$ square unit.

Find the area when $y=8$ .

Substitute 8 for $y$ in the expression $y^2-2y-3$ .

  $\begin{array}{c}\text{Area}=y^2-2y-3\\ =8^2-2\times 8-3\\ =64-16-3\\ =45\end{array}$

Hence, the area of the platform is 45 square unit.