Question 93 (i)

The following expression is the area of a rectangle. Find the possible length and breadth of the rectangle.

$x^{2} - 6 x + 8$

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Solution

Given area of a rectangle= $x^{2} - 6 x + 8$
Now, we have to find the possible length and breadth of the rectangle.
So, we factorise the given expression.
i.e. $x^{2} - 6 x + 8 = x^{2} - (4 + 2) x + 8 = x^{2} - 4 x - 2 x + 8 = x (x - 4) - 2 (x - 4) = (x - 4) (x - 2)$
Since, area of rectangle = Length $\times$ Breadth. Hence, the possible length and breadth are (x-2) and (x-4) .

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