Answer:
[tex]x^2-50x+456=0[/tex]
Step-by-step explanation:
GIVEN: A [tex]100\text{ foot}[/tex] fence is used to enclose a rectangular land plot. If the area of the land plot is [tex]456\text{ feet}^2[/tex].
TO FIND: equation to determine the length [tex]x[/tex] of the land plot.
SOLUTION:
total length of fence [tex]=100\text{ foot}[/tex]
let the width of land plot be [tex]y[/tex]
perimeter of plot [tex]=2(x+y)=100[/tex]
[tex]x+y=50[/tex]
area of rectangular plot [tex]=\text{length}\times\text{breadth}[/tex]
[tex]xy=456[/tex]
[tex]y=\frac{456}{x}[/tex]
putting value of [tex]y[/tex]
[tex]x+\frac{456}{x}=50[/tex]
[tex]x^2-50x+456=0[/tex]
Hence required equation to get length [tex]x[/tex] of land plot is [tex]x^2-50x+456=0[/tex]
on solving
[tex]x=38,12[/tex]
possible length of land plot is [tex]38\text{ foot}[/tex] and [tex]12\text{ foot}[/tex]
