Find X in a Parallelogram: Perimeter 10 with Side Length X-2

Below is a parallelogram.

AB = 4

AC = X-2

The perimeter of the parallelogram is 10.

Calculate X.

Video Solution

Solution Steps

00:00 Find X

00:03 Opposite sides are equal in parallelograms

00:11 They are also a pair of opposite sides, therefore equal

00:24 Values of all sides

00:33 The perimeter of the parallelogram equals the sum of its sides

00:48 Let's substitute appropriate values and solve for X

01:02 Group the numbers to one side, and X to one side

01:14 Isolate X

01:25 And this is the solution to the question

Step-by-Step Solution

The problem involves calculating $X$ for a parallelogram with given side lengths and perimeter. Let's proceed step-by-step:

Step 1: First, recognize that in a parallelogram, opposite sides are equal:
- $AB = CD = 4$ (given)
- $AC = BD = X-2$

Step 2: Use the perimeter formula for the parallelogram:
$P = 2(a + b)$
where $a = AB = 4$ and $b = AC = X-2$ .

Step 3: Plug the perimeter value and side lengths into the formula:
$10 = 2(4 + (X - 2))$

Step 4: Simplify and solve for $X$ :
$10 = 2(4 + X - 2)$
$10 = 2(X + 2)$

Step 5: Divide both sides by 2 to eliminate the factor:
$5 = X + 2$

Step 6: Subtract 2 from both sides to isolate $X$ :
$X = 3$

Therefore, the correct value of $X$ is $3$ .

The corresponding choice is option 4.