Question

The area of a rectangular field is $30 \, m^2$. If its length is $1 \, m$ greater than its breadth $x$, then the quadratic equation to find them will be:

• A. $x^2 + x + 30 = 0$
• B. $x^2 - x + 30 = 0$
• C. $x^2 + x - 30 = 0$
• D. $x^2 - x - 30 = 0$

Hint:

When solving rectangle problems, always form the equation using $\text{Area} = \text{Length} \times \text{Breadth}$. Carefully translate word statements into algebraic expressions.

Answer 1

The Correct Option is C

Step 1: Represent dimensions
Let the breadth of the rectangle be $x$ m.
Then, length $= x+1$ m.

Step 2: Write the area condition
\[ \text{Area} = \text{Length} \times \text{Breadth} \] \[ 30 = x(x+1) \]

Step 3: Simplify into quadratic form
\[ 30 = x^2 + x \] \[ x^2 + x - 30 = 0 \]

Step 4: Conclusion
Thus, the quadratic equation is: \[ \boxed{x^2 + x - 30 = 0} \]