Reynaldo cut a triangle out of paper. The lengths of the sides of the triangle are 8 inches, 5.5 inches, and 4.5 inches. Next, he wants to cut out a rectangle that will have the same perimeter as the triangle. Calculate the combined length of the two adjacent sides of a rectangle with the same perimeter. Show your work
The perimeter of the triangle is the sum of its three sides:
Perimeter = 8 + 5.5 + 4.5 = 18 inches
Since the rectangle will have the same perimeter as the triangle, its perimeter will also be 18 inches.
Let the length of the rectangle be L inches and the width be W inches. The perimeter of a rectangle is given by:
Perimeter = 2(L + W)
Given that the perimeter is 18 inches, we have:
2(L + W) = 18
L + W = 9
We want to find the combined length of the two adjacent sides of the rectangle, which is L + L = 2L. From the previous equation, we can solve for L:
L + W = 9
L = 9 - W
Substituting this into the equation 2L = 18:
2(9 - W) = 18
18 - 2W = 18
-2W = 0
W = 0
Since the width cannot be 0, it seems there might be a mistake in our calculations or the problem statement. Let me try again.