if an office has an area of 120 sqare feet and a perimeter of 44 feet. what are the dimensions of this office.
add all sides together=perimeter
p=10+10+12+12
length*width=area
10*12=120
The perimeter of a square office is 120 feet. How long is each side of the office?
To find the dimensions of the office, we can set up a system of equations based on the given information.
Let's assume the length of the office is represented by "L" and the width is represented by "W".
Given:
Area of the office = 120 square feet
Perimeter of the office = 44 feet
The formula for the area of a rectangle is Length * Width, so we have the equation:
L * W = 120
The formula for the perimeter of a rectangle is 2 * (Length + Width), so we have the equation:
2 * (L + W) = 44
Now, we can solve this system of equations to find the values of L and W.
Solving the first equation for L, we get L = 120/W.
Substituting this value of L into the second equation, we have:
2 * (120/W + W) = 44
Expanding this equation, we get:
240/W + 2W = 44
Multiplying all terms by W to clear the fraction, we have:
240 + 2W^2 = 44W
Rearranging the equation, we get:
2W^2 - 44W + 240 = 0
Factoring this quadratic equation, we have:
2(W - 10)(W - 12) = 0
Setting each factor equal to zero, we get two possible solutions:
W - 10 = 0 -> W = 10
W - 12 = 0 -> W = 12
So, the possible widths of the office are 10 feet and 12 feet.
Now, substituting these values of W back into the first equation, L * W = 120, we can find the corresponding lengths.
For W = 10:
L * 10 = 120
L = 12
For W = 12:
L * 12 = 120
L = 10
Therefore, the dimensions of the office are:
Length = 12 feet and Width = 10 feet, or
Length = 10 feet and Width = 12 feet.