Respuesta :
The equation for the area of the rectangle is given by:
A=40w - w²
But the value of the area A = 300
Substitute the value of A into the equation
300= 40w - w²
Rearrange the equation
w² - 40w + 300 = 0
The above is now a quadratic equation
To find the width, simply solve for w in the above quadratic equation.
Using the formula method to solve the above quadratic equation;
[tex]w=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]w² - 40w + 300 = 0
a=1 b=-40 and c=300
substitute the values into the formula and evaluate
[tex]w=\frac{-(-40)\pm\sqrt[]{(-40)^2-4(1)(300)}}{2(1)}[/tex][tex]=\frac{40\pm\sqrt[]{1600-1200}}{2}[/tex][tex]=\frac{40\pm\sqrt[]{400}}{2}[/tex][tex]=\frac{40\pm20}{2}[/tex][tex]=\frac{40}{2}\pm\frac{20}{2}[/tex][tex]=20\pm10[/tex]Either w = 20 + 10 or w= 20 - 10
w = 30 or w=10
This implies that there are two possible values for the width of the rectangle
Let's check our answer
p = 2l + 2w
80 = 2l + 2w
40 = l + w
If w = 30
l = 40 - 30 = 10
A = l x w = 10 x 30 = 300 m²
If w=10
l=40 - 10 = 30
A = l x w = 30 x 10 = 300 m²
Therefore, the width of the rectangle is either 30m or 10 m
