Find X When Two Trapezoids Have Equal Perimeters: 5X + 2X-2 + 6X Solution

Video Solution

Solution Steps

00:00 Find X

00:03 The perimeter of the trapezoid equals the sum of its sides

00:07 Let's substitute appropriate values according to the given data and solve for the perimeter

00:18 Let's gather all possible factors

00:31 This is the perimeter size of trapezoid 1

00:36 Now let's use the same method to find the perimeter of trapezoid 2

00:49 Let's gather all possible factors

00:58 This is the perimeter size of trapezoid 2

01:01 The perimeters of the trapezoids are equal according to the given data

01:05 Now let's compare the perimeters and solve for X

01:10 Let's move X to the left side and numbers to the right side of the equation

01:21 And this is the solution to the problem

Step-by-Step Solution

To solve this problem, we'll follow these steps:

Let's work through the steps:

Step 1: Calculate the perimeter of each trapezoid.

For the first trapezoid, the perimeter is:

$5X + (2X - 2) + (X - 1) + 6X = 14X - 3$

For the second trapezoid, the perimeter is:

$(2X + 1) + 4X + (4X + 1) + 3X = 13X + 2$

Step 2: Set the two perimeter expressions equal:

$14X - 3 = 13X + 2$

Step 3: Solve for $X$ .

Subtract $13X$ from both sides:

$X - 3 = 2$

Add 3 to both sides:

$X = 5$

Therefore, the solution to the problem is $X = 5$ .