SOLUTION: the length of a rectangle is 8 ft. longer than the width. Which has the same dimension as the side of a square . if the area of the rectangle is equal to 160 square feet more than

Algebra ->  Rectangles -> SOLUTION: the length of a rectangle is 8 ft. longer than the width. Which has the same dimension as the side of a square . if the area of the rectangle is equal to 160 square feet more than       Log On


   

Question 635434: the length of a rectangle is 8 ft. longer than the width. Which has the same dimension as the side of a square . if the area of the rectangle is equal to 160 square feet more than the area of the square. What are the length and width of the rectangle?
Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!
Area of Rectangle (A)=Length(L)*Width(W) or A(Rectangle)=LW
Area of a Square (A)=Side(S)* Side(S) or A(square)=S^2
Let W=width of rectangle which is also the length of the side of a square
Then the length,L, of the rectangle=W+8
Area, A, of rectangle=W(W+8)
Area of Square=W^2
Now we are told the following:
W^2+160=W(W+8) simplify
W^2+160=W^2+8W collect like terms (W^2's cancel out)
8W=160
W=20 ft------------------width of rectangle
W+8=20+8=28 ft----Length of rectangle
CK
20*28=20*20+160
560=400+160
560=560
Hope this helps----ptaylor