Mathematics: The area of a rectangular plot is 136 square meters. the length of the plot (in meters) is one more than twice its width. find the length and width of the plot.

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The area of a rectangular plot is 136 square meters.

deadpoolcorvettehats

12.03.2022

Let the width of the plot be 'x' meters and length be 'y' meters.

According to the question, the length of the plot (in meters) is one more than twice its width.

So, y=1+2x

Area of rectangular plot = $length \times width$

= $(1+2x) \times x$

= x + 2x^2

Since, area of rectangular plot = 136 square meters.

136 = x+2x^2

2x^2+x-136=0

2x^2-16x+17x-136=0

2x(x-8)+17(x-8)=0

(2x+17)(x-8)=0

So, x-8=0 or (2x+17)=0

So, x =8 or $x = \frac{-17}{2}$

Since, width can not be negative.

Therefore, width of the rectangular plot = x = 8 meters

So, length of the rectangular plot = y = 1+2x = $1+(2 \times 8)$ = 17 meters.

Therefore, the length and width of the rectangular plot are 17 meters and 8 meters respectively.

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