Question

A 100 - foot fence is used to enclose a rectangular land plot. If the area of the land plot is 456 square feet, which equation can be used to determine the length (x) of the land plot?

Answer 1

Answer:

$x^2-50x+456=0$

Step-by-step explanation:

GIVEN: A $100\text{ foot}$ fence is used to enclose a rectangular land plot. If the area of the land plot is $456\text{ feet}^2$.

TO FIND: equation to determine the length $x$ of the land plot.

SOLUTION:

total length of fence $=100\text{ foot}$

let the width of land plot be $y$

perimeter of plot $=2(x+y)=100$

                            $x+y=50$

area of rectangular plot $=\text{length}\times\text{breadth}$

                                       $xy=456$

                                      $y=\frac{456}{x}$

putting value of $y$

$x+\frac{456}{x}=50$

$x^2-50x+456=0$

Hence required equation to get length $x$ of land plot is $x^2-50x+456=0$

on solving

$x=38,12$

possible length of land plot is $38\text{ foot}$ and $12\text{ foot}$