The top of a rectangular table has an area of 224 square feet. It has a length that is 2 feet more than the width. Find the dimensions of the table top.
w(w+2) = 224
w^2 + 2 w - 224 = 0
(w-14)(w+16) =0
w = 14
To find the dimensions of the table top, we can set up an equation based on the given information.
Let's say the width of the table top is x feet.
According to the problem, the length of the table top is 2 feet more than the width, so the length can be expressed as (x + 2) feet.
The area of a rectangle is calculated by multiplying its length by its width. In this case, the area is given as 224 square feet. Therefore, we have the equation:
Length × Width = Area
(x + 2) × x = 224
Now, we can solve this equation to find the dimensions of the table top.
Expanding the equation, we get:
x^2 + 2x = 224
Rearranging the equation, we have:
x^2 + 2x - 224 = 0
To solve this quadratic equation, we can factor it or use the quadratic formula.
Factorizing the equation, we find:
(x - 14)(x + 16) = 0
Setting each factor equal to zero, we get:
x - 14 = 0 or x + 16 = 0
Solving for x, we find two possible values for the width of the table top:
x = 14 or x = -16
Since the width cannot be negative in this context, we discard the negative value. Therefore, the width of the table top is 14 feet.
Substituting this value back into the equation for the length, we have:
Length = x + 2 = 14 + 2 = 16 feet
So, the dimensions of the table top are 14 feet by 16 feet.