A square table with an area of 25 sq ft is pushed together with a rectangular table with an area of 40 sq ft. What is the perimeter of the new table?
I assume the rectangular table measures 5 by 8 feet.
P = 2L + 2W
P = 2(13) + 2(5)
P = ?
First, I read this problem twice. I noticed that the following info was given in the problem. Use complete sentences.
The square table measures 5 feet on each side. I assume the rectangular table measures 5 by 8 feet.
By pushing the tables together, we have one table measuring 5 by 13 feet.
To find the perimeter of the new table, we first need to determine the dimensions of the rectangular table when it is pushed together with the square table.
Let's assume the side length of the square table is 's' feet. Since the area of a square is given by the formula A = s^2, we can solve for 's' by taking the square root of the area:
s = √(25 sq ft)
s = 5 ft
Now, let's assume the rectangular table has length 'L' feet and width 'W' feet. Since the area of a rectangle is given by the formula A = L × W, we can solve for either 'L' or 'W' by dividing the area by the other dimension:
40 sq ft = L × W
Now we need to consider the combined area of the two tables. The new table will have a combined area of 25 sq ft (from the square table) plus 40 sq ft (from the rectangular table):
Combined area = 25 sq ft + 40 sq ft
Combined area = 65 sq ft
Since the combined area is equal to the length times the width (L × W), we can substitute the values:
L × W = 65 sq ft
Now we need to find the dimensions of the rectangular table when it is pushed together with the square table. We can do this by solving the equation L × W = 65 sq ft using different values for 'L' and 'W':
L = 13 ft, W = 5 ft
L = 5 ft, W = 13 ft
Since the table is essentially a rectangle, it doesn't matter which dimension is considered the length or the width, so we can use the values L = 13 ft and W = 5 ft.
Now that we have the dimensions of the new table, we can calculate its perimeter by using the formula 2L + 2W:
Perimeter = 2(13 ft) + 2(5 ft)
Perimeter = 26 ft + 10 ft
Perimeter = 36 ft
Therefore, the perimeter of the new table is 36 feet.