If the area of a rectangular field is 21x2 – 7x and one of its sides is 7x, what is its other side?

1. Break Down the Problem

We need to determine the unknown side of a rectangular field given its area and one known side.

Given:

• Area = $21x^2 - 7x$
• One side = $7x$

2. Relevant Concepts

The area $A$ of a rectangle can be expressed by the formula: $A = \text{length} \times \text{width}$ In this case, if one side is $7x$, the other side can be represented as: $\text{Other Side} = \frac{A}{\text{One Side}}$ Thus: $\text{Other Side} = \frac{21x^2 - 7x}{7x}$

3. Analysis and Detail

Let's perform the calculation: $\text{Other Side} = \frac{21x^2 - 7x}{7x}$ We can simplify this by dividing each term in the numerator by $7x$: $= \frac{21x^2}{7x} - \frac{7x}{7x}$ Calculating each term:

1. $\frac{21x^2}{7x} = 3x$
2. $\frac{7x}{7x} = 1$

Putting it together, we get: $\text{Other Side} = 3x - 1$

4. Verify and Summarize

We have simplified the expression, and the calculations checked out.

Final Answer

The other side of the rectangular field is $3x - 1$.