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Relationship between LCM and GCD

Question 40 G...

Question

Question 40
Give a possible expression for the length and breadth of the rectangle whose area is given by $4 a^{2} + 4 a - 3$ .

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Solution

Given, area of rectangle = $= 4 a^{2} + 4 a - 3$
$4 a^{2} + 6 a - 2 a - 3$ [by splitting middle term]
$= 2 a (2 a + 3) - 1 (2 a + 3) = (2 a - 1) (2 a - 3)$ [Area of rectangle= $l \times b$ ]
Hence, possible length = 2a - 1,Breadth = 2a + 3 or vice versa

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Relationship between LCM and GCD

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