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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Updated on: 10-Oct-2022

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