Parallelogram Perimeter: Finding the Total Length When One Side is 0.5X

Given a parallelogram in which the length of one side is 2 times the length of the other side and given that the length of the larger side is 0.5X:

AAABBBDDDCCC

Express by X the perimeter of the parallelogram.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:11 Let's express the perimeter of a parallelogram using X.
00:15 Remember, in a parallelogram, opposite sides are equal.
00:26 Now, consider the larger pair of sides.
00:31 Let's look at the side length given in the problem.
00:37 And check the ratio of the sides provided.
00:42 We'll substitute the side value to find the length A C.
00:58 Again, remember that opposite sides are equal in a parallelogram.
01:16 The perimeter is simply the sum of all the sides of the parallelogram.
01:30 Now, substitute the correct values and solve for the perimeter.
01:43 And that's how we solve this problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Given a parallelogram in which the length of one side is 2 times the length of the other side and given that the length of the larger side is 0.5X:

AAABBBDDDCCC

Express by X the perimeter of the parallelogram.

2

Step-by-step solution

To solve the problem, follow these steps:

  • Step 1: Identify the given side lengths.
    The longer side of the parallelogram is given as 0.5X0.5X. The other side, being half the length of the long side, is 0.25X0.25X.
  • Step 2: Use the perimeter formula.
    The formula for the perimeter PP of a parallelogram is P=2a+2bP = 2a + 2b, where aa and bb are the lengths of the sides.
  • Step 3: Plug in the side lengths into the formula.
    Substitute a=0.5Xa = 0.5X and b=0.25Xb = 0.25X into the perimeter formula:
    P=2(0.5X)+2(0.25X)=X+0.5X=1.5XP = 2(0.5X) + 2(0.25X) = X + 0.5X = 1.5X.

Thus, the perimeter of the parallelogram expressed in terms of XX is 1.5X1.5X.

Therefore, the correct answer is choice 22, which is 1.5X1.5X.

3

Final Answer

1.5X

Practice Quiz

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Given the parallelogram:

444222AAABBBDDDCCC

Calculate the perimeter of the parallelogram.

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