SOLUTION: A rectangle field is going to be completely enclosed by 100m of fencing. Determine the dimensions of the field that will result in an area of 575m square. Round your answer to the

Question 390023: A rectangle field is going to be completely enclosed by 100m of fencing. Determine the dimensions of the field that will result in an area of 575m square. Round your answer to the nearest tenth of a metre.
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
A rectangle area:
....where and are length and width
given:
and for fencing which is equal to perimeter
to find: and
use
and and solve the system

...solve for
........substitute in and find

...both sides multiply by

...solve for

Solved by pluggable solver: Quadratic Formula

Let's use the quadratic formula to solve for x:

Starting with the general quadratic

the general solution using the quadratic equation is:

So lets solve ( notice , , and )

Plug in a=-1, b=50, and c=-575

Square 50 to get 2500

Multiply to get

Combine like terms in the radicand (everything under the square root)

Simplify the square root (note: If you need help with simplifying the square root, check out this solver)

Multiply 2 and -1 to get -2

So now the expression breaks down into two parts

or

Now break up the fraction

or

Simplify

or

So the solutions are:

or

one solution