Mathematics: 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?

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A 100 - foot fence is used to enclose a rectangular

narnia85

23.01.2022

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 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 $=\text{length}\times\text{breadth}$

xy=456

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

putting value of

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

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 $12\text{ foot}$

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