$Given the area of rectangle is A = 25 a^{2} - 35 a + 69. The length is given as (5 a - 3) . Find the width of the rectangle.$

$5 a - 3$

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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
$5 a - 4$

$Let y be the width.$
$Given: Area = 25 a^{2} - 35 a + 69$

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

$Hence, y \times (5 a - 3) = 25 a^{2} - 35 a + 69$
$y = (25 a^{2} - 35 a + 69) \div (5 a - 3)$
By long division method,

$5 a - 3 5 a - 23) ¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯ 25 a^{2} - 35 a + 69 25 a^{2} - 12 a - + ¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯ - 23 a + 69 - 23 a + 69 + - ¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯ 0$
$∴ y = 5 a - 23 Width of the rectangle = 5 a - 23$

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