Question

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.

Answer 1

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 * width`

=
`(1+2x) * 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 = (-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 * 8)` = 17 meters.

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

Answer 2

Let the length of the rectangular field be x meter

Width of the rectangular field be y meter .

It is given that the length is 1 more than twice its width.

So, x = 1+2y

Area of rectangle = length * width

`(1+2y)*y=136`

`2y^2+y = 136`

`2y^2+y-136 = 0`

Using factoring to solve the equation.

The middle term y is split as 17y - 16y so that 17 * -16 = -272 (2*-136)

`2y^2-16y+17y-132 =0`

`2y(y-8)+17(y-8)`=0[/tex]

`(2y+17)(y-8) = 0`

Equating each factor to 0 gives y=8 or y= -17/2

Since y depicts the width here, we neglect the negative term.

Width of the rectangle is 8 feet

Length = 1+2(8) = 17 feet.