Find the possible length and breadth of a rectangle whose area is $(x^{2} + 9 x + 20)$ square units.

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Solution

$x^{2} + 9 x + 20 = x^{2} + (5 + 4) x + (5 \times 4)$

[Using the identity $(x + a) (x + b) = x^{2} + (a + b) x + a b$ ]

$= (x + 4) (x + 5)$

The length and breadth of the rectangles are $(x + 4)$ units and $(x + 5)$ units or $(x + 5)$ units and $(x + 4)$ units.

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