Solve for X: Rectangle with Perimeter 48 and Dimensions (3-x) and (8+2x)

Video Solution

Solution Steps

00:05 Let's find the value of X in the rectangle.

00:09 Remember, opposite sides are equal in a rectangle.

00:14 The whole side equals the sum of its parts.

00:18 So, let's plug in the values we know to find the side length.

00:27 Great! This is the side length of the rectangle.

00:33 Now, the perimeter is the total of all the sides added up.

00:40 Insert the known perimeter value, according to the information we have, to solve for X.

00:47 Let's gather all the like terms together.

00:50 We need to get X by itself now.

00:53 And that's how we solve this problem! Well done!

Step-by-Step Solution

To solve the problem of finding $x$ given the perimeter of rectangle ABCD, we follow these steps:

Step 1: The problem states that the perimeter of rectangle ABCD is 48. The expressions related to $x$ represent sides of this rectangle.
Step 2: Identify the sides using expressions in the diagram:
- The complete top and bottom sides (width) are divided into $3-x$ and full vertical is $5+x$ .
- One vertical height is $8+2x$ .
Step 3: Use the perimeter formula for a rectangle: $P = 2(\text{width} + \text{height})$ .
Step 4: Substitute in the formula and solve for $x$ .

Now, let's apply these steps:

Express the perimeter using the given: $2((3-x) + (5+x)) + 2(8+2x) = 48$ .

Simplify the equation:

$2(3-x + 5+x) + 2(8+2x) = 48$

$2(8) + 2(8+2x) = 48$

$16 + 16 + 4x = 48$

Combine like terms:

$32 + 4x = 48$

Isolate $4x$ :

$4x = 48 - 32$

$4x = 16$

Solve for $x$ :

$x = \frac{16}{4}$

$x = 4$

Therefore, the value of $x$ is $x = 4$ .