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Give possible expression for the length and breadth of the rectangle having $35y^2 + 13y - 12$ as its area.
Given :
Area of a rectangle is given by $35y^2 + 13y - 12$.
To do :
We have to find possible expressions for the length and breadth of the rectangle.
Solution :
We know that,
Area of a rectangle of length $l$ and breadth $b$ is $lb$.
Therefore, factorizing the given expression, we get,
Area $=35y^2 + 13y - 12$
$=35y^2+ 28y- 15y- 12$ [Since $35 \times(-12)=-420=28 \times(-15), 13=28-15$]
$=7 y(5 y+4)-3(5 y+4)$
$= (5 y+4)(7 y-3)$
If length $= 5y + 4$, then breadth $= 7y - 3$
If length $= 7y-3$, then breadth $= 5y+ 4$
Hence, possible expressions for the length and breadth of the rectangle are $(5 y+4)$ and $(7 y-3)$.
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