Give possible expression for the length and breadth of the rectangle whose area is : $25 a^{2} - 35 a + 12$

(5 a + 2) (5 a - 3)

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(5 a - 3) (5 a - 4)

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(5 a - 1) (5 a - 2)

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None

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Solution

The correct option is B $(5 a - 3) (5 a - 4)$
Given area of rectangle is $25 a^{2} - 35 a + 12$
Let length and breadth is $l$ and $b$
then area of rectangle $= l b =$ $25 a^{2} - 35 a + 12$
$= 25 a^{2} - 20 a - 15 a + 12$
$= 5 a (5 a - 4) - 3 (5 a - 4)$
$= (5 a - 4) (5 a - 3)$
So, length $= (5 a - 3)$
And breadth $= (5 a - 4)$ .

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