The area of a rectangle is $25 a^{2} - 35 a + 12$ . If the length is given as $5 a - 3$ , then the width is .

4 a - 5

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a - 4

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5 a - 4

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5 a - 3

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Solution

The correct option is C $5 a - 4$
Let $y$ be the width.

Since area is given as $25 a^{2} - 35 a + 12$ which is the product of $y$ and $(5 a - 3),$ we have
$y (5 a - 3) = 25 a^{2} - 35 a + 12.$

To find y, we need to divide $25 a^{2} - 35 a + 12$ by $5 a - 3.$
$\begin{matrix} 5 a - 4 5 a - 3 25 a^{2} - 35 a + 12 25 a^{2} - 15 a - --------------- - - 20 a + 12 - 20 a + 12 - ---------- - 0 \end{matrix}$ $∴ y = 5 a - 4$ .

Hence, the width of the rectangle is $(5 a - 4)$ .

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