Question

3.4
score: 11/12 answered: 11/12
question 12
a rectangle has length $x^{2}-x + 6$ units and width $x + 1$ units. find $x$ such that the area of the rectangle is 24 square units.
$x=$
question help: ebook written example

Explanation:

Step1: Recall area formula

The area $A$ of a rectangle is $A = \text{length}\times\text{width}$. So, $(x^{2}-x + 6)(x + 1)=24$.

Step2: Expand the left - hand side

Using the distributive property (FOIL for binomials extended), we have $x^{3}+x^{2}-x^{2}-x+6x + 6=24$. Simplifying gives $x^{3}+5x+6 = 24$, or $x^{3}+5x-18=0$.

Step3: Try integer values

We try some simple integer values of $x$. When $x = 2$, $2^{3}+5\times2-18=8 + 10-18=0$.

Answer:

$x = 2$