Give possible expression for the length and breadth of the rectangle having $35 y^{2} + 13 y - 12$ as its area.

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Solution

Area of a rectangle $= 35 y^{2} + 13 y - 12 35 y^{2} + 28 y - 15 y - 12 ⎧ ⎪ ⎨ ⎪ ⎩ \begin{matrix} ∵ 35 \times (- 12) = - 420 ∴ - 420 = 28 \times (- 15) 13 = 28 - 15 \end{matrix} ⎫ ⎪ ⎬ ⎪ ⎭ = 7 y (5 y + 4) - 3 (5 y + 4) = (5 y + 4) (7 y - 3)$

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\begin{matrix} \begin{matrix} A r e a : 25 a^{2} - 35 a + 12 \end{matrix} (i) \end{matrix} \begin{matrix} \begin{matrix} A r e a : 35 y^{2} + 13 y - 12 \end{matrix} (i i) \end{matrix}

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Give possible expression for the length and breadth of the rectangle having 35y2+13y−12 as its area.

Area of a rectangle=35y2+13y−1235y2+28y−15y−12⎧⎪⎨⎪⎩∵35×(−12)=−420∴−420=28×(−15)13=28−15⎫⎪⎬⎪⎭=7y(5y+4)−3(5y+4)=(5y+4)(7y−3)

Give possible expression for the length and breadth of the rectangle having $35 y^{2} + 13 y - 12$ as its area.

Area of a rectangle $= 35 y^{2} + 13 y - 12 35 y^{2} + 28 y - 15 y - 12 ⎧ ⎪ ⎨ ⎪ ⎩ \begin{matrix} ∵ 35 \times (- 12) = - 420 ∴ - 420 = 28 \times (- 15) 13 = 28 - 15 \end{matrix} ⎫ ⎪ ⎬ ⎪ ⎭ = 7 y (5 y + 4) - 3 (5 y + 4) = (5 y + 4) (7 y - 3)$