The area of a rectangular courtyard is $(10 x^{3} - 11 x^{2} + 19 x + 10)$ sq units. If one of its sides is $(2 x^{2} - 3 x + 5)$ units, then the other side is

(5 x + 2)

units

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- 5 x + 2

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- (5 x + 2)

units

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5 x - 2

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Solution

The correct option is A $(5 x + 2)$ units
Given, area of a rectangular courtyard $= (10 x^{3} - 11 x^{2} + 19 x + 10)$ sq. units.
One side $= (2 x^{2} - 3 x + 5)$
Let the other side of the rectangle be $y$ cm
Area of a rectangle $=$ length $\times$ breath
$\Rightarrow (10 x^{3} - 11 x^{2} + 19 x + 10) = (2 x^{2} - 3 x + 5) y$
$\Rightarrow y = \frac{10 x^{3} - 11 x^{2} + 19 x + 10}{2 x^{2} - 3 x + 5}$

$5 x + 2$
$2 x^{2} - 3 x + 5$ $10 x^{3} - 11 x^{2} + 19 x + 10$
$10 x^{3} - 15 x^{2} + 25 x$
$4 x^{2} - 6 x + 10$
$4 x^{2} - 6 x + 10$
$0$
Thus, $y = 5 x + 2$

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