Final answer:
To solve for x in the context of a rhombus with side lengths x and 8x-49, set the two expressions equal because all sides of a rhombus are equal. Solving the equation x = 8x - 49, you find that x is equal to 7.
Step-by-step explanation:
Finding the Side Length of a Rhombus
In a rhombus, all sides are of equal length. If one side length is x and another is described by the expression 8x - 49, then we set the expressions equal to each other because the lengths must be the same. Thus:
x = 8x - 49
Next, we will solve for x. Subtract 8x from both sides to get:
-7x = -49
Next, divide both sides by -7:
x = 7
Therefore, the value of x that makes the side lengths equal is 7.