## Pages

### 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