Give possible expressions for the length and breadth of each of the following rectangles, in which their areas are given: Area : 25 $a^{2}$ – 35a + 12

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Solution

Since area of rectangle = length $\times$ breadth. Let us factorize the following equations into two terms.

Area = 25 $a^{2}$ – 35a + 12

= 25 $a^{2}$ – 15a - 20a + 12 (Using splitting method)

= 5a(5a -3) - 4(5a - 3)

= (5a - 3)(5a -4)

$∴$ Possible length = (5a - 3)

and Possible width = (5a -4)

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25 a^{2} - 35 a + 12

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Give possible expressions for the length and breadth of each of thefollowing rectangles, in which their areas are given:

\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}

\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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