Question

The area of a rectangular field is 260 square meters. If its length becomes 5 meters less and breadth 2 meters more, it becomes a square field. Find the length and breadth of the rectangular field.

Hint:

When a rectangle is modified into a square, set length equal to breadth plus/minus changes.

Answer 1

Let the original length and breadth of the rectangular field be \( l \) and \( b \).
Given:
\[ l \times b = 260. \] When modified:
\[ (l - 5) = (b + 2). \] Thus,
\[ l - 5 = b + 2. \] \[ l - b = 7. \] Solving \( l \times b = 260 \) and \( l - b = 7 \):
Substituting \( l = b + 7 \) in the area equation:
\[ (b+7) \times b = 260. \] \[ b^2 + 7b - 260 = 0. \] Using the quadratic formula:
\[ b = \frac{-7 \pm \sqrt{49 + 1040}}{2} = \frac{-7 \pm 33}{2}. \] \[ b = 13, \quad l = 20. \] Thus, \( l = 20 \) meters, \( b = 13 \) meters.