Answer:
L = 20 feet
W = 7 feet
Explanation:
Let W and L be the Width and Length of the rectangle, respectively. A is the area of the rectangle (A = W*L)
We are told that W = L - 7 ft
We also find that A = 260 ft^2
Since A = W*L, lets write:
A = 260 ft^2
W*L = 260 ft^2
We know from the first equation that W = L - 7', so use that definition of L in the above equation:
W*L = 260 ft^2
(L-7ft)*L = 260 ft^2
L^2 - 7Lft = 260 ft^2
L^2 - 7Lft - 260 ft^2 = 0
Solve using the quadratic equation:
L = 20 and L = -13
We can drop the - 13 feet, leaving only L = 20 feet
Since W = L - 7 ft, W must be 13 feet
CHECK:
Is the width 7 ft less than the length?
L = 20
W = 7
Yes: The width is 7 feet less than the length
Is the area 260 ft^2?
(20')*(13) = 260 ft^2
Yes: The area is 260 ft^2