A rectangular balcony has an area of 32 square feet and a perimeter of 24 feet. What are the dimensions of the balcony?
4*8
To find the dimensions of the balcony, we'll need to set up a system of equations based on the given information.
Let's assume the length of the rectangle is L and the width is W.
From the problem statement, we have two pieces of information:
1. The area of the balcony is 32 square feet, so we can write the equation: L * W = 32
2. The perimeter of the balcony is 24 feet, so we can write the equation: 2 * (L + W) = 24
Now we can solve this system of equations.
Let's rearrange the second equation to isolate L:
2 * L + 2 * W = 24
2 * L = 24 - 2 * W
L = 12 - W
Substitute this expression for L into the first equation:
(12 - W) * W = 32
Expanding the equation:
12W - W^2 = 32
Rearranging to form a quadratic equation:
W^2 - 12W + 32 = 0
This equation can be solved using factoring, completing the square, or the quadratic formula. Let's use factoring in this case:
(W - 4)(W - 8) = 0
So, either W - 4 = 0 or W - 8 = 0
If W - 4 = 0, then W = 4
If W - 8 = 0, then W = 8
We have two possible values for W. Now let's calculate the corresponding values for L.
When W = 4, using L = 12 - W:
L = 12 - 4 = 8
So one possible dimension is W = 4 and L = 8.
When W = 8, using L = 12 - W:
L = 12 - 8 = 4
So the other possible dimension is W = 8 and L = 4.
Therefore, the balcony can have dimensions of either 4 feet by 8 feet or 8 feet by 4 feet.
A = LW
P = 2L + 2W
What are the factors of 32?
2 * 16
4 * 8
Which of those measurements would give us the perimeter of 24 feet?