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:

Express by X the perimeter of the parallelogram.

Video Solution

Solution Steps

00:00 Express the perimeter of the parallelogram using X

00:03 Opposite sides are equal in a parallelogram

00:15 The larger pair of sides

00:20 The side length according to the given data

00:26 The ratio of sides according to the given data

00:31 Substitute the side value to find AC

00:47 Opposite sides are equal in a parallelogram

01:05 The perimeter of the parallelogram equals the sum of its sides

01:19 Substitute appropriate values and solve to find the perimeter

01:32 And this is the solution to the question

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 $0.5X$ . The other side, being half the length of the long side, is $0.25X$ .
Step 2: Use the perimeter formula.
The formula for the perimeter $P$ of a parallelogram is $P = 2a + 2b$ , where $a$ and $b$ are the lengths of the sides.
Step 3: Plug in the side lengths into the formula.
Substitute $a = 0.5X$ and $b = 0.25X$ into the perimeter formula:
$P = 2(0.5X) + 2(0.25X) = X + 0.5X = 1.5X$ .

Thus, the perimeter of the parallelogram expressed in terms of $X$ is $1.5X$ .

Therefore, the correct answer is choice $2$ , which is $1.5X$ .