Question

instructions
choose the best answer. if necessary, use the paper you were given.
question
the expressions $x - 4$ and $x + 2$ represent the length and width of a rectangle, respectively. if the area of the rectangle is 27, what is the perimeter of the rectangle?
a 22
b 24
c 27
d 31

Explanation:

Step1: Find the value of x using area formula

The area of a rectangle is $A = length\times width$. So, $(x - 4)(x + 2)=27$. Expand the left - hand side: $x^{2}+2x-4x - 8 = 27$, which simplifies to $x^{2}-2x-35 = 0$. Factor the quadratic equation: $(x - 7)(x+5)=0$. So, $x=7$ or $x=-5$. Since length and width cannot be negative in this context, we take $x = 7$.

Step2: Find the length and width

When $x = 7$, the length $l=x - 4=7 - 4 = 3$ and the width $w=x + 2=7 + 2 = 9$.

Step3: Calculate the perimeter

The perimeter of a rectangle is $P=2(l + w)$. Substitute $l = 3$ and $w = 9$ into the formula: $P=2(3 + 9)=2\times12=24$.

Answer:

B. 24