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

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Solution

Let y be the width of the rectangle
$∴ y (5 a - 3) = 25 a^{2} - 35 a + 12$ [0.5 Mark]

To find y, we need to divide $25 a^{2} - 35 a + 12$ by $(5 a - 3)$ .
$5 a - 3 5 a - 4 \sqrt{25 a^{2} - 35 a + 12} 25 a^{2} - 15 a (-) (+) ¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯ - 20 a + 12 - 20 a + 12 (+) (-) ¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯ 0$
$∴ y = 5 a - 4$ [2 Marks]

Hence, the width of the rectangle is $5 a - 4$ . [0.5 Mark]

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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.

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

25 a^{2} - 35 a + 12

5 a - 3

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