How many different rectangles with integral measurements can be drawn with perimeter as 32
To find the number of different rectangles with integral measurements that can be drawn with a perimeter of 32, we can go through the possible dimensions and count the number of rectangles for each case.
Let's start by considering the dimensions of a rectangle. We know that the perimeter of a rectangle is given by the formula: Perimeter = 2 * (length + width).
Given that the perimeter is 32, we have the equation: 2 * (length + width) = 32.
Now, let's list down the possible values for length and width that satisfy this equation:
1. Length = 1, Width = 15: In this case, the perimeter is 2 * (1 + 15) = 32. So, we have one rectangle.
2. Length = 2, Width = 14: Again, the perimeter is 2 * (2 + 14) = 32. So, we have one rectangle.
3. Length = 3, Width = 13: The perimeter is 2 * (3 + 13) = 32. So, we have one rectangle.
4. Length = 4, Width = 12: The perimeter is 2 * (4 + 12) = 32. So, we have one rectangle.
We can continue this process and find the possible dimensions until we reach Length = 16, Width = 1 (since swapping length and width would give the same rectangle).
By going through these possibilities, we find that there are a total of 16 rectangles with integral measurements that can be drawn with a perimeter of 32.