Question

Find the area of the rectangle shown. Write the answer in simplest form.

Short answer

The area of the rectangle is $xy$.

Step-by-step solution

Step 1. Define the concept.

Area of rectangle is given by product of its length and breadth.

Step 2. Divide by the common factors before multiplying.

From the figure it can be deduced that the length of the rectangle is$\frac{y^2}{2x}$ and the breadth of the rectangle is$\frac{2x^2}{y}$.

Area =$\frac{y^2}{2x}\cdot \frac{2x^2}{y}$

Step 3. Simplify the expression.

Further simplify the expression.

$$\begin{gathered} A=\frac{2x^2}{y}\cdot \frac{y^2}{2x} \\ =\frac{x^{2-1}}{1}\cdot \frac{y^{2-1}}{1} \\ =xy \end{gathered}$$

Therefore, the area of the rectangle is $xy$.