Question

The length of a rectangle is 2 units more than the width. The area of the rectangle is 24 units. What is the width, in units, of the rectangle?

Answer 1

Answer:

$2\sqrt{5}$

Step-by-step explanation:

So, we know the area is 24, and the length is 2 more than the width. Let's refer to the width as x, and the length as x+2. In a rectangle, area is length times width. So, let's multiply the length and width to get x$x^{2}$ + 4. This is because any number times itself is that number squared. Now that we have that, solve for x. Subtract 4 from both sides of the equation and get x$x^{2} +4.$ Now we have $x^{2} =20$. What we do next is do the square root of both sides, in order to get x by itself. this gives us the answer of $\sqrt{24}$. That is the width of the rectangle. If you want to go further, we can simplify the expression. 20 is 4*5, and 4 is a square number. We can rewrite the expression now as x=$\sqrt{4} *\sqrt{5}$. We know the square root of 4 is 2, but the square root of 5 is too difficult to work with and get an exact answer, so we can leave that as-is. our final answer for the width of the rectangle is $2\sqrt{5}$. I hope this helps!