SOLUTION: The side of a square equals the width of a rectangle. The length of the rectangle is 10 meters longer than its width. The sum of the areas of the square and the rectangle is 208 sq

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: The side of a square equals the width of a rectangle. The length of the rectangle is 10 meters longer than its width. The sum of the areas of the square and the rectangle is 208 sq      Log On


   

Question 1067205: The side of a square equals the width of a rectangle. The length of the rectangle is 10 meters longer than its width. The sum of the areas of the square and the rectangle is 208 square meters. Find the side of the square.
Answer by chen.aavaz(62) About Me  (Show Source):
You can put this solution on YOUR website!

Side of square a = w
Length of rectangle l=w%2B10
Area of square A+=+a%5E2+=+w%5E2
Area of rectangle R+=+l%2Aw+=+%28w%2B10%29%2Aw
Sum of A+R=208 so
w%5E2%2B%28w%2B10%29%2Aw=208
w%5E2%2Bw%5E2%2B10w-208=0
2w%5E2%2B10w-208=0
w%5E2%2B5w-104=0
w=%28-5%2B-sqrt%285%5E2-4%2A1%2A104%29%29%2F%282%2A1%29
The equation has two roots, w=8 and w=-13. Obviously we keep only the positive.
So the side of the square is 8m.