Given the area of rectangle is $A = 25 a^{2} - 45 a + 18$ . The length is given as ( $5 a - 3$ ). Therefore, the width is:

5a - 3

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5a - 4

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4a - 5

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a - 4

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Solution

The correct option is A
5a - 3

Let y be the width.
Since area is given as $25 a^{2} - 45 a + 18$ which is the product of $y$ and $(5 a - 3),$ we have
$y (5 a - 3) = 25 a^{2} - 45 a + 18$
To find y, we need to do a long division of $25 a^{2} - 45 a + 18$ by (5a-3).
$5 a - 3 5 a - 6 \sqrt{25 a^{2} - 45 a + 18} 25 a^{2} - 15 a - + ¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯ - 30 a + 18 - 30 a + 18 + - ¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯ 0$
$∴ y = 5 a - 6$

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