SOLUTION: a rectangular room has an area of 189 square feet and a perimeter of 55 feet. what are the dimensions of the room? Find exact solution.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: a rectangular room has an area of 189 square feet and a perimeter of 55 feet. what are the dimensions of the room? Find exact solution.      Log On


   

Question 134544: a rectangular room has an area of 189 square feet and a perimeter of 55 feet. what are the dimensions of the room? Find exact solution.
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
Formula for Area of a rectangle? A = l*w
Formula for perimeter of a rectangle? P = 2l + 2w
Given A = 189, P = 55
189+=+l%2Aw
55+=+2l+%2B+2w
189%2Fw+=+l+
55+=+2%28189%2Fw%29+%2B+2w+
55+=+378%2Fw+%2B+2w+
55w+=+378+%2B+2w%5E2
0+=+2w%5E2+-+55w+%2B+378
Use the quadratic equation
w+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
w+=+%2855+%2B-+sqrt%28+55%5E2-4%2A2%2A378+%29%29%2F%282%2A2%29+
w+=+%2855+%2B-+sqrt%28+3025-3024+%29%29%2F%282%2A2%29+
w = 54/4, 56/4
w = 13.5
l = 14