Rectangle Perimeter Problem: Solve for X When Sides are (x-10) and (4x-8)

To solve this problem, we'll use the perimeter of a rectangle formula:

• Step 1: Identify the side lengths.
• Step 2: Use the perimeter formula to set up the equation.
• Step 3: Solve for $x$.

Now, let's work through each step:

Step 1: The side lengths are $x - 10$ and $4x - 8$.
Step 2: The perimeter $P$ is given by $2(x - 10) + 2(4x - 8) = 24$.

Simplify the equation:

$2(x - 10) + 2(4x - 8) = 24$ $2x - 20 + 8x - 16 = 24$

Combine like terms:

$10x - 36 = 24$

Step 3: Solve for $x$:

$10x = 24 + 36$ $10x = 60$ $x = 6$

Therefore, the value of $x$ is $\boxed{6}$.