Question

instructions
choose the best answer. if necessary, use the paper you were given.
question
a rectangle has a length of $x + 4$ and a width of $x - 3$. if the area of the rectangle is 30, what is the perimeter of the rectangle?
a 24
b 26
c 28
d 32

Explanation:

Step1: Find the value of x

The area of a rectangle is given by length times width. So, $(x + 4)(x - 3)=30$.
Expand the left - hand side: $x^{2}-3x + 4x-12 = 30$, which simplifies to $x^{2}+x-12 - 30=0$, or $x^{2}+x - 42 = 0$.
Factor the quadratic equation: $(x + 7)(x - 6)=0$.
So, $x=-7$ or $x = 6$. Since length and width cannot be negative in this context, we take $x = 6$.

Step2: Find the length and width

Length $l=x + 4=6 + 4=10$.
Width $w=x - 3=6 - 3=3$.

Step3: Calculate the perimeter

The perimeter of a rectangle is $P = 2(l + w)$.
Substitute $l = 10$ and $w = 3$ into the formula: $P=2(10 + 3)=2\times13 = 26$.

Answer:

B. 26