SOLUTION: the area of a rectangular field is 94m^2. its perimeter is 38 meters. find the dimension of the field.

Algebra ->  Rectangles -> SOLUTION: the area of a rectangular field is 94m^2. its perimeter is 38 meters. find the dimension of the field.      Log On


   

Question 898964: the area of a rectangular field is 94m^2. its perimeter is 38 meters. find the dimension of the field.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Try solving this in general.
A for area, p for perimeter.
Dimensions x and y.

Rectangle.
xy=A and 2x%2B2y=p.
Assume A and p are known.
2y=p-2x
y=%28p-2x%29%2F2
y=p%2F2-x------substitute this into the area equation.
-
x%28p%2F2-x%29=A
%28P%2F2%29x-x%5E2-A=0
-x%5E2%2B%28p%2F2%29x-A=0 and multiply both members by -1.
highlight_green%28x%5E2-%28p%2F2%29x%2BA=0%29
which, if you substitute for the values of p and A now, you might find that the
quadratic expression is factorable; but you do not always have this condition.

x=%28p%2F2%2B-+sqrt%28%28p%2F2%29%5E2-4%2AA%29%29%2F2
You most likely want the PLUS square root form;
highlight%28x=%28p%2F2%2Bsqrt%28%28p%2F2%29%5E2-4A%29%29%2F2%29

Use the area equation to solve for y.
y=A%2Fx
A%2F%28%28p%2F2%2Bsqrt%28%28p%2F2%29%5E2-4A%29%29%2F2%29
highlight%28y=%282A%29%2F%28p%2F2%2Bsqrt%28%28p%2F2%29%5E2-4A%29%29%29

You can substitute for A and p early and avoid pure symbolic form, but if the quadratic expression is
not factorable, the solution in pure symbolic form will work for all problems of this general kind.