2.Find the areas of rectangles with the following pairs of monomials as their lengths and breadths respectively.

\((p, q); (10m, 5n); (20x^2, 5y^2); (4x, 3x^2); (3mn, 4np)\)

\((p, q); (10m, 5n); (20x^2, 5y^2); (4x, 3x^2); (3mn, 4np)\)

(i) Given that: Length = p units and breadth = q units

Area of the rectangle = \(length \times breadth = p \times q = pq\) sq units

(ii)Given that: Length = 10 m units, breadth = 5n units

∴Area of the rectangle =\(length \times breadth = 10 m \times 5 n = (10 \times 5) \times m \times n = 50 mn\; \)sq units

(iii) Given that: Length = 20x2 units, breadth = 5y2 units

∴Area of the rectangle = length × breadth = 20x2 × 5y2 = (20 × 5) × x2 × y2 = 100x2y2 sq units

(iv)Given that: Length = 4x units, breadth = 3x2 units

∴Area of the rectangle = \(length \times breadth = 4x \times 3x^2 = (4 \times 3) \times x \times x^2 = 12x^3\;\) sq units

(v) Given that: Length = 3mn units, breadth = 4np units

∴Area of the rectangle = \(length \times breadth = 3mn \times 4np = (3 \times 4) \times mn \times np = 12mn^2p\;\) sq units