Answer
The wide of a strip he should cultivate is 4ft
Given
A farmer has a 100 ft by 50 ft rectangular field that he wants to increase by 25.28% by cultivating a strip of uniform width around the current field
Solution
Since, the increment is by 25.28%
[tex]\frac{(100+2w)(50+2w)-100(50)}{100(50)}=0.2528[/tex]We cross multiply and solve for w
[tex]\begin{gathered} \frac{(100+2w)(50+2w)-100(50)}{100(50)}=0.2528 \\ \\ \frac{(100+2w)(50+2w)-100(50)}{5000}=0.2528 \\ \text{Cross multiply} \\ (100+2w)(50+2w)-100(50)=0.2528\times5000 \\ (100+2w)(50+2w)-5000=0.2528\times5000 \\ \text{open the bracket} \\ 5000+200w+100w+4w^2-5000=1264 \\ collect\text{ like terms } \\ 200w+100w+4w^2-5000+5000=1264 \\ 300w+4w^2=1264 \\ 4w^2+300w-1264=0 \\ \text{Divide all through by 4} \\ w^2+75w-316=0 \\ \end{gathered}[/tex]We can now solve the quadratic equation by factorisation
[tex]\begin{gathered} w^2-4w+79w-316=0 \\ (w^2-4w)+(79w-316)=0 \\ w(w^{}-4)+79(w-4)=0 \\ (w-4)\text{ (w+79)=0} \\ w=4 \\ w=-79 \\ \end{gathered}[/tex]Distance can't be negative
Therefore, the wide of a strip he should cultivate is 4ft
