1. A rectangular yard is to be enclosed by 400 m of fence on three sides. An existing wall is on the fourth side. The area of the yard is to be 450 m^2. Determine the dimensions of the yard.
Assume that the width is the side parallel to the wall.
Then the perimeter of the fence is:
Since the total length of the three sides is 400m, then
the value of perimeter is 400.
Then, solve for w.
`400-2l=w` (Let this be EQ1.)
Next, use the given area to set-up the second equation.
Set one side equal to zero.
To simplify, divide both sides by 2.
Then, use the quadratic formula to solve for l.
So, values of l are:
`l=198.869` and `l = 1.131`
Next, solve for w. To do so, plug-in the values of l to EQ1.
Hence, the three sides of the rectangular yard can have either the following dimensions:
`198.869 xx 198.869 xx 2.262` meters or
`1.131xx 1.131xx 1.131` meters.