A rectangular table is six times as long as it is wide. If the area is 96ft^2, find the length and the width of the table
x * 6x = 96
x^2 = 16
...
Let's represent the width of the table as "w" feet.
The length of the table is given as six times the width, which means the length is 6w feet.
The area of a rectangle is calculated by multiplying the length by the width. In this case, the area is 96ft^2.
So we can set up the equation:
length * width = area
(6w) * w = 96
Now we can solve for w.
6w^2 = 96
Divide both sides of the equation by 6:
w^2 = 16
Taking the square root of both sides, we get:
w = ±4
Since width cannot be negative in this context, we only consider the positive value.
Therefore, the width of the table is 4 feet.
To find the length, we can substitute the value of the width into the equation:
length = 6w = 6 * 4 = 24 feet
Thus, the length of the table is 24 feet and the width is 4 feet.
To find the length and width of the table, we can use the information given.
Let's assume the width of the table is "w" and the length is "l".
We are given that the table is six times as long as it is wide. So we can write the equation:
l = 6w
Now we know that the area of a rectangle is given by the formula:
Area = length × width
We are given that the area is 96 sq.ft, so we can write the equation:
96 = l × w
Substituting the value of l from the first equation into the second equation, we have:
96 = 6w × w
Now we can solve this equation to find the width of the table.
96 = 6w^2
Divide both sides by 6:
16 = w^2
Taking the square root of both sides, we get:
w = ±4
Since the width cannot be negative, we take the positive solution:
w = 4 ft
Substituting this back into the first equation, we can find the length:
l = 6w
l = 6 × 4
l = 24 ft
Therefore, the length of the table is 24 ft and the width is 4 ft.