a rectangle table is five times as long as it is wide if the area is 245 feet ^2 find the length and width of the table
width -- x
length -- 5x
x(5x) = 245
5x^2 = 245
x^2 = 49
x = ± 7
To find the length and width of the rectangle table, we can set up an equation using the given information.
Let's assume the width of the table is represented by 'w'.
Given that the rectangle table is five times as long as it is wide, we can express the length as 5w.
The formula for the area of a rectangle is length multiplied by width:
Area = Length × Width
Substituting the values, we can write the equation as:
245 = (5w) × w
Now, we can solve for 'w' by rearranging the equation and simplifying:
245 = 5w^2
Divide both sides of the equation by 5:
49 = w^2
Next, take the square root of both sides to isolate 'w':
√49 = √w^2
This gives us two possible solutions: w = 7 and w = -7. Since the width of a rectangle cannot be negative, we discard the negative solution.
Therefore, the width of the rectangle table is 7 feet.
To find the length, we can substitute this value of width back into the equation:
Length = 5w
Length = 5(7)
Length = 35 feet
So, the length of the rectangle table is 35 feet, and the width is 7 feet.