Respuesta :
10feet
Given:
A farmer has a 25 ft by 100 ft rectangular field that he wants to reduce to 16% of its original size.
To find how wideof a strip he can cut around the edge of his field to do this.
Let w be the width of a strip should he cut around the edge to reduce to 16%
Original area = 25 x 100 = 2500 ft²
Hence;
(25 - 2w)(100 - 2w)= 16% of 2500
(25 - 2w)(100 - 2w) = 0.16 x 2500
(25 - 2w)(100 - 2w) =400
Open the parenthesis.
2500 - 50w - 200w + 4w² = 400
Rearrange in the form of quadratic equation.
2500 - 250w + 4w² - 400 = 0
2100 - 250 w + 4w² = 0
4w² - 250w + 2100 = 0
Divide through by 2
2w² - 125w + 1050 = 0
We can now solve the above using using the quadratic formula.
a = 2 b=-125 c=1050
[tex]w=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex][tex]w=\frac{125\pm\sqrt[]{15625-8400}}{4}[/tex][tex]=\frac{125\pm\sqrt[]{7225}}{4}[/tex][tex]=\frac{125\pm85}{4}[/tex][tex]\begin{gathered} \text{Either } \\ w=\frac{125+85}{4}=\frac{210}{4}=52.5 \\ \\ or \\ \\ w=\frac{125-85}{4}=\frac{40}{4}=10 \end{gathered}[/tex]Let's check for the reasonable solution.
(25 - 2w)(100 - 2w) = 400
w=10
(25 - 20)(100 - 20) = (5)(80) = 400
The only reasonable solution is w= 10
Therefore, the widthof the strip should be 10 feet.
