A rectangular-shaped dance floor has a perimeter of 164 feet. If the floor were 44 feet wider, its width would equal its length. Find the length and width of the dance floor.

l = w + 44

2w + 2l = 164

Do same process as previous post.

To find the length and width of the dance floor, we can set up a system of equations based on the given information. Let's assume the length of the original dance floor is 'L' feet and the width is 'W' feet.

According to the problem statement, we are told that the rectangular floor has a perimeter of 164 feet. The perimeter of a rectangle is calculated by adding the lengths of all four sides. So, we can write the equation:

2L + 2W = 164 ...equation 1

We are also given that if the floor were 44 feet wider, its width would equal its length. This means that the new width would be W + 44 feet, and it would be equal to the length L. This can be expressed as:

W + 44 = L ...equation 2

Now, we have a system of two equations (equation 1 and equation 2), and we can solve them simultaneously to find the values of L and W.

Let's solve the system of equations:

From equation 2, we can rewrite it as L = W + 44.

Substituting this value into equation 1, we get:

2(W + 44) + 2W = 164

Simplifying the equation:

2W + 88 + 2W = 164
4W + 88 = 164

Subtracting 88 from both sides:

4W = 76

Dividing both sides by 4:

W = 19

Now, we can substitute the value of W into equation 2 to find the length L:

L = W + 44
L = 19 + 44
L = 63

Therefore, the length of the dance floor is 63 feet and the width of the dance floor is 19 feet.