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 lan…

Question

asked May 16, 2021 56.8k views

1 Answer

Dhaval Patel · Answer 1 · 2021-05-21T06:54:19+0000

Answer:

x^2-50x+456=0

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
of the land plot.

SOLUTION:

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

let the width of land plot be

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

x+y=50

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

xy=456

y=(456)/(x)

putting value of

x+(456)/(x)=50

x^2-50x+456=0

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

on solving

x=38,12

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