Using information given in the following figure, find the length and breadth of this rectangle in cm.[Figure: a rectangle whose top side is \(5m + n\), bottom side is \(2m + 3n + 5\), left side is \(m + n - 3\) and right side is \(3m - 2n + 7\), all…

Answer: length = 43 cm, breadth = 12 cm

In a rectangle, opposite sides are equal.

\(5m + n = 2m + 3n + 5\), i.e. \(3m - 2n = 5\) ...... (1)

\(m + n - 3 = 3m - 2n + 7\), i.e. \(-2m + 3n = 10\) ...... (2)

Multiply (1) by 3 : \(9m - 6n = 15\); multiply (2) by 2 : \(-4m + 6n = 20\).

Adding : \(5m = 35\), so \(m = 7\).

From (1) : \(3(7) - 2n = 5\), so \(2n = 16\), \(n = 8\).

Length \(= 5m + n = 35 + 8 = 43\) cm (check bottom : \(2(7) + 3(8) + 5 = 43\) ✓).

Breadth \(= m + n - 3 = 7 + 8 - 3 = 12\) cm (check right : \(3(7) - 2(8) + 7 = 12\) ✓).