Chapter 8.6, Problem 3P

To determine

To find the possible dimensions of the rectangle using factoring method.

Answer to Problem 3P

The possible dimensions of the rectangle is $\left(4x+5\right)\left(2x+3\right).$

Explanation of Solution

Given information :

Area of rectangle is $8x^2+22x+15$

Since we have $8x^2+22x+15$

Now the middle term can be written as sum of $2$ terms such that whose product is equal to first term $\left(8x^2\right)\times$ last term $\left(15\right)$ , so the required two terms are $10x$ and $12x$ .

i.e. $22x=10x+12x$

  $\begin{array}{l}\Rightarrow 8x^2+22x+15=8x^2+10x+12x+15\\ =2x\left(4x+5\right)+3(4x+5)\\ =\left(4x+5\right)\left(2x+3\right)\end{array}$

Therefore, the area of rectangle is $8x^2+22x+15$

  $\Rightarrow$ $\text{length}\times \text{width}=\left(4x+5\right)\left(2x+3\right)$

Hence, the possible dimensions of the rectangle is $\left(4x+5\right)\left(2x+3\right).$