Calculate X: Rectangle Area = 22x with Side Length (x+8)

Looking at the diagram, one side is labeled as $x+8$ (the length), so the other side must be $\frac{1}{2}x$ (the width) to give us the area formula $22x = \frac{1}{2}x \times (x+8)$.

When we factor $\frac{1}{2}x(x-36) = 0$, we get x = 0 or x = 36. But x = 0 would mean the rectangle has no width, so it wouldn't exist! Only x = 36 makes sense in this context.

The diagram shows $x+8$ labeled on one side. Since Area = length × width and we're told Area = $22x$, the unlabeled side must be $\frac{22x}{x+8}$, which simplifies to $\frac{1}{2}x$ when x = 36.

Yes! You could use the quadratic formula on $\frac{1}{2}x^2 - 18x = 0$, but factoring is much faster here since we can factor out $\frac{1}{2}x$ immediately.

Double-check your algebra! The most common error is incorrectly distributing $\frac{1}{2}x \times (x+8)$. Make sure you get $\frac{1}{2}x^2 + 4x$, then subtract to get $\frac{1}{2}x^2 - 18x = 0$.