The top of a rectangular table has an area of 255 square feet. It has a length that is 2 feet more than the width. Find the dimensions of the table top.
width ----- x
length ---- x+2
area=width * length
x(x+2) = 255
x^2 + 2x - 255 = 0
can you think of two numbers that are two apart and multiply to get 255 ?
Hint: they would be "close" to √255
To find the dimensions of the table top, let's represent the width as "x" feet.
According to the given information, the length of the table top is 2 feet more than the width, so it can be represented as "x + 2" feet.
To find the area of the table top, we multiply the length by the width:
Area = Length x Width
Since the area is given as 255 square feet, we can set up the equation:
255 = (x + 2) * x
Now, let's solve the equation to find the value of "x", which represents the width:
255 = x^2 + 2x
To solve this quadratic equation, we rearrange it in standard form:
x^2 + 2x - 255 = 0
Now, we can either factor the quadratic equation or use the quadratic formula. In this case, factoring is less straightforward, so let's use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
For our equation, a = 1, b = 2, and c = -255. Substituting these values into the quadratic formula:
x = (-2 ± √(2^2 - 4 * 1 * -255)) / (2 * 1)
Simplifying further:
x = (-2 ± √(4 + 1020)) / 2
x = (-2 ± √(1024)) / 2
x = (-2 ± 32) / 2
This gives us two possible values for the width:
x₁ = (-2 + 32) / 2 = 30 / 2 = 15
x₂ = (-2 - 32) / 2 = -34 / 2 = -17
Since we are dealing with a physical dimension, the width cannot be negative. Therefore, we discard the negative value.
So, the width of the table top is 15 feet.
We can now use this value to find the length:
Length = Width + 2 = 15 + 2 = 17 feet.
Therefore, the dimensions of the table top are 15 feet by 17 feet.