Question
Give possible expressions for the length and breadth of the rectangle whose area is given by $4a^2 + 4a - 3.$
✓
Answer
Given, area of rectangle $= 4a^2 + 6a - 2a - 3$
$= 4a^2 + 4a - 3 [$by splitting middle term$]$
$= 2a(2a + 3) - 1(2a + 3) = (2a - 1)(2a + 3)$
Hence, possible length $= 2a - 1$ and breadth $= 2a + 3$
$= 4a^2 + 4a - 3 [$by splitting middle term$]$
$= 2a(2a + 3) - 1(2a + 3) = (2a - 1)(2a + 3)$
Hence, possible length $= 2a - 1$ and breadth $= 2a + 3$
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