the length of the top of a table is 6 m greater than the width. the area is 91m^2. Find the dimensions of the table.
(w+6)*w=91
solve for w first, then l (which is w+6)
I would use the quadratic equation.
To find the dimensions of the table, we need to set up an equation based on the given information.
Let's assume the width of the table is 'x' meters. According to the problem, the length of the top of the table is 6 meters greater than the width. Therefore, the length can be represented as 'x + 6' meters.
The area of a rectangle is calculated by multiplying the length and width. In this case, we are given that the area is 91 square meters. So, we can set up the equation:
Area = Length × Width
91 = (x + 6) × x
Now, we have a quadratic equation. Let's solve it:
91 = x^2 + 6x
Rearranging the equation:
x^2 + 6x - 91 = 0
To solve this quadratic equation, we can factor it or use the quadratic formula. Let's use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
For our equation: a = 1, b = 6, and c = -91. Substituting these values into the formula:
x = (-6 ± √(6^2 - 4(1)(-91))) / (2(1))
x = (-6 ± √(36 + 364)) / 2
x = (-6 ± √400) / 2
x = (-6 ± 20) / 2
Now, we have two possible solutions for the width, denoted as x1 and x2:
x1 = (-6 + 20) / 2
x1 = 14 / 2
x1 = 7
x2 = (-6 - 20) / 2
x2 = -26 / 2
x2 = -13
Since width cannot be negative, we discard the negative value (-13) for x2.
Therefore, the width of the table (x) is 7 meters.
Now, we can find the length by substituting the value of x into the expression we derived earlier:
Length = x + 6
Length = 7 + 6
Length = 13
So, the dimensions of the table are 7 meters (width) and 13 meters (length).