The sides of two square plots are $(2 x - 1)$ m and $(5 x + 4)$ . The area of the second square plot is $9$ times the area of the first square plot. Find the side of the smaller plot.

15

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13

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31

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39

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Solution

The correct option is B $13$ m
Area of first plot = Area of second plot
$\Rightarrow 9 {(2 x - 1)}^{2} = {(5 x + 4)}^{2} \Rightarrow 3 (2 x - 1) = (5 x + 4) \Rightarrow 6 x - 3 = 5 x + 4 \Rightarrow x = 7$
Therefore, side of larger plot = $(5 \times 7 + 4) = 39 m$
side of smaller plot = $2 \times 7 - 1 = 13 m$

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