Help with parallelogram


In the diagram below, PQRS is a parallelogram with a perimeter of 26 and an area of 28. What is the perimeter of rectangle OSTQ?  Include an explanation of how you solved the problem.

 Mar 5, 2023

Unfortunately, since there is no diagram provided, I am unable to solve the problem accurately. However, I can provide a general method for solving this type of problem involving finding the perimeter of a rectangle given the dimensions of a parallelogram.

To find the perimeter of a rectangle given a parallelogram with known dimensions, follow these steps:

1. Find the height of the parallelogram by dividing the area by the base. In other words, if the base of the parallelogram is "b" and the height is "h", then:

   area = base x height
   28 = b x h
   h = 28/b

2. Use the perimeter of the parallelogram to find the length of one side. Since the opposite sides of a parallelogram are equal in length, we can divide the perimeter by 2 to get the length of one side. If the perimeter is "P" and one side is "s", then:

   P = 2s + 2b
   s = (P - 2b)/2

3. Since the rectangle has the same width as the parallelogram, the length of the rectangle is equal to the length of one side of the parallelogram. So the perimeter of the rectangle is:

   perimeter = 2(s + b)

By substituting the values we found for "s" and "h" from steps 1 and 2 into this equation, we can solve for the perimeter of the rectangle.

I hope this helps!

 Mar 5, 2023

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