Question

The area of a rectangular field is 30 m². If its length is 1 m greater than its breadth, 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 a problem involves the area of a rectangle and one dimension is expressed in terms of the other, set up a quadratic equation and solve for the unknown dimension.

Answer 1

The Correct Option is D

Let the breadth of the rectangle be \(x\) meters. Then the length will be \(x + 1\) meters. The area of a rectangle is given by: \[ \text{Area} = \text{Length} \times \text{Breadth} \] Given that the area is 30 m², we have: \[ (x + 1) \times x = 30 \] Simplifying the equation: \[ x^2 + x = 30 \] Rearrange to get the quadratic equation: \[ x^2 + x - 30 = 0 \] Thus, the quadratic equation to find the length and breadth is \( x^2 + x - 30 = 0 \). The correct answer is (C).