Parallelogram Perimeter: Expressing Length X + (X+4) Solution

Question

Given a parallelogram where the length of one side is greater by 4 than the length of another side and given that the length of the smaller side is X:

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Express by X the perimeter of the parallelogram.

Video Solution

Solution Steps

00:12 Let's express the perimeter of the parallelogram using the variable X.
00:17 Remember, opposite sides are equal in a parallelogram.
00:25 Let's look at the larger pair of sides.
00:29 Here, the side length is given in the problem.
00:37 We also have a side ratio provided in the problem.
00:41 Now, let's substitute the side value to calculate side AB.
00:48 Again, note that opposite sides are equal in a parallelogram.
00:57 The perimeter is the sum of all sides of the parallelogram.
01:12 Insert the given values and solve for the perimeter.
01:20 And that's how we solve this problem!

Step-by-Step Solution

To solve the problem, we'll apply the perimeter formula for a parallelogram. We are given that one side a=X a = X and the other side b=X+4 b = X + 4 . The perimeter P P of a parallelogram is calculated by the formula:

P=2(a+b) P = 2(a + b)

Substitute the values of a a and b b :
a=X a = X
b=X+4 b = X + 4

Plug these into the formula:

P=2(X+(X+4)) P = 2(X + (X + 4))

Simplify the expression inside the parentheses:

P=2(2X+4) P = 2(2X + 4)

Distribute the 2:

P=4X+8 P = 4X + 8

Therefore, the perimeter of the parallelogram in terms of X X is 4X+8 4X + 8 .

Answer

4X+8

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Perimeter of a Parallelogram: Using variables