Question

the length of a rectangle is the sum of the width and 1. the area of the rectangle is 30 square units. what is the length, in units, of the rectangle?

Explanation:

Step1: Define variables

Let the width of the rectangle be $w$ units. Then the length $l = w + 1$ units.

Step2: Set up area - formula equation

The area of a rectangle is $A=l\times w$. Given $A = 30$, we substitute $l$ and $A$ into the formula: $(w + 1)\times w=30$.

Step3: Expand the equation

$w^{2}+w - 30=0$.

Step4: Factor the quadratic equation

$(w + 6)(w - 5)=0$.

Step5: Solve for $w$

$w+6 = 0$ gives $w=-6$ (rejected since width cannot be negative), $w - 5=0$ gives $w = 5$.

Step6: Find the length

Since $l=w + 1$ and $w = 5$, then $l=5 + 1=6$.

Answer:

6