$Given the area of rectangle is A = 25 a^{2} - 35 a + 12. The length is given as (5 a - 3) . Find the width of the rectangle.$

$5 a - 3$

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$5 a - 4$

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$4 a - 5$

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$a - 4$

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Solution

The correct option is B
$5 a - 4$

$Let y be the width.$
$Given: Area = 25 a^{2} - 35 a + 12$

$We know that, area of a rectangle$ $= Length \times breadth$

$Hence, y \times (5 a - 3) = 25 a^{2} - 35 a + 12$
$y = (25 a^{2} - 35 a + 12) \div (5 a - 3)$
By long division method,

$5 a - 3 5 a - 4) ¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯ 25 a^{2} - 35 a + 12 25 a^{2} - 15 a - + ¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯ - 20 a + 12 - 20 a + 12 + - ¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯ 0$
$∴ y = 5 a - 4 Width of the rectangle = 5 a - 4$

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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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