Fourth Proportional of x, 2x, (x+1) is:
Proportions are equal ratios. In this problem, we are given three quantities: x, 2x, and (x+1). We need to find the fourth proportional of these quantities.
Step 1: Write the Proportion
Let the fourth proportional be y. Then, we can write the proportion as:
x : 2x :: (x+1) : y
Step 2: Cross Multiply
Cross multiplying the above proportion, we get:
x*y = 2x*(x+1)
Step 3: Solve for y
Simplifying the above equation, we get:
y = (2x*(x+1))/x
y = 2(x+1)
Therefore, the fourth proportional of x, 2x, and (x+1) is 2(x+1).
Explanation
To find the fourth proportional of x, 2x, and (x+1), we used the concept of proportionality. We know that if four quantities are in proportion, then their ratios are equal. Using this concept, we set up a proportion between x, 2x, (x+1), and the fourth proportional y. We then cross multiplied the proportion and solved for y. The final answer we obtained was 2(x+1).