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The perimeter of a rectangle is 100feet and the area is 400feet what is the dimensions of the rectangle?
Area can't be in "feet"; I'll assume it is "square feet".
Solve two simultaneous equations:
Perimeter: 2(a+b) = 100
Area: ab = 400
Solve perimeter equation for one variable:
2(a+b) = 100
a+b = 50
a = 50 - b
Substitute this in the other equation:
ab = 400
(50-b)b = 400
50b - b2 = 400
b2 -50b+400 = 0
To continue, use the quadratic formula, factoring, or complete the square. In this case, factoring is easy, so:
(b-40)(b-10) = 0
"b" can be either 40 or 10. Replacing in the equation ab = 400, "a" is either 10 or 40.
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