A rectangular is six times as long as it is wide. If the area is 54 ft^2, find the length and the width of the table.
let x = width
let 6x = length (according to the first statement)
recall that area of a rectangle is given by,
A = length x width
thus,
54 = x * 6x
54 = 6x^2
9 = x^2
x = 3 ft (width)
6x = 18 ft (length)
hope this helps~ :)
Let's assume the width of the table is "x" ft.
Since the length is six times the width, the length of the table can be represented as 6x ft.
The formula for calculating the area of a rectangle is length multiplied by width, so we can write the equation:
Area = Length × Width
54 = 6x × x
To solve this equation, we need to rearrange it in standard quadratic form:
6x^2 = 54
Next, divide both sides of the equation by 6 to isolate x^2:
x^2 = 54/6
x^2 = 9
Now, take the square root of both sides to find the value of x:
x = √9
x = 3
Therefore, the width of the table is 3 ft.
To find the length, we can substitute the value of x back into the equation for the length:
Length = 6x
Length = 6 × 3
Length = 18
So, the length of the table is 18 ft.
In conclusion, the width of the table is 3 ft and the length is 18 ft.
To find the length and width of the table, we can set up an equation based on the information given.
Let's assume the width of the table is "w" feet. Since the length is six times the width, the length would be "6w" feet.
The formula for the area of a rectangle is given by:
Area = Length × Width
We are given that the area is 54 ft^2, so we can substitute the values into the formula:
54 = (6w) × w
Now, we can solve this equation to find the width (w) of the table:
54 = 6w^2
Divide both sides by 6:
9 = w^2
Taking the square root of both sides:
w = ±√9
Since width cannot be negative, we discard the negative value, and we get:
w = 3 ft
Now that we know the width is 3 ft, we can find the length (L) by multiplying 6 with the width:
L = 6w = 6 * 3 = 18 ft
Therefore, the length of the table is 18 ft and the width is 3 ft.