99.6k views
2 votes
The width of a rectangle is 7 ft less than the length. The area of the rectangle is 260 ft2. Find the length L and width W of the rectangle. L =_____ ft W = _____ft

User Shanieka
by
7.8k points

1 Answer

6 votes

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

User Kevin Carrasco
by
8.2k points