Word problems on Quadratic Equations (5)

Area of a rectangular plot is `200m^2` and perimeter is `60` meter. If length of plot is given in x meter. Use the perimeter 60 meter to write the value of width in terms of x. Find the dimensions of the plot.

Solution:

Given:

• Perimeter = 60 meter
• Area = `200m^2`
• Length = x meter

Area = length * width

`200 = x * w`
`200/x = w`

Perimeter = 2(length + width)

`60 = 2(x + 200/x)`
`60 = 2x + 400/x`
`60 = (2x^2 + 400)/x`
`60x = 2x^2 + 400`
`-2x^2 + 60x - 400 = 0`
`-2(x^2 - 30x + 200 = 0`
`x^2 -20x - 10x + 200 = 0`
`x(x - 20) -10(x - 20) = 0`
`x - 20 = 0`     `x - 10 = 0`
`x = 20`          ` x = 10`

Length is `20` meter and width is `200/20 = 10` meter

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