The area of a rectangle is $A = 25 a^{2} - 35 a + 12$ . Its length is ( $5 a - 3$ ), find its width.

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Solution

Let y be the width of the rectangle
$∴ y (5 a - 3) = 25 a^{2} - 35 a + 12$
To find y, we need to divide $25 a^{2} - 35 a + 12$ by $(5 a - 3)$ .
$5 a - 3 5 a - 4 \sqrt{25 a^{2} - 35 a + 12} 25 a^{2} - 15 a (-) (+) ¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯ - 20 a + 12 - 20 a + 12 (+) (-) ¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯ 0$
$∴ y = 5 a - 4$
Hence, the width of the rectangle is $5 a - 4$

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