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Question
The following expression is the area of a rectangle. Find the possible length and breadth of the rectangle.
x2 – 6x + 8
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Solution
Given, area of a rectangle = x2 – 6x + 8
Now, we have to find the possible length and breadth of the rectangle.
So, we factorise the given expression.
i.e. x2 – 6x + 8 = x2 – (4 + 2)x + 8
= x2 – 4x – 2x + 8
= x(x – 4) – 2(x – 4)
= (x – 4)(x – 2)
Since, area of a rectangle = Length × Breadth.
Hence, the possible length and breadth are (x – 4) and (x – 2).
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