If 25, z, z, 49 are in proportion, then find the value of z.

Answer

To find the value of \( z \) in the proportion \( 25, z, z, 49 \), we can set up the proportion as follows:

1. **Understanding Proportions**: In a proportion, the ratio of the first two terms is equal to the ratio of the last two terms. Therefore, we can write:
\[ \frac{25}{z} = \frac{z}{49} \]

2. **Cross Multiplying**: To solve for \( z \), we will cross multiply:
\[ 25 \cdot 49 = z \cdot z \]
This simplifies to:
\[ 1225 = z^2 \]

3. **Taking the Square Root**: Now, we will take the square root of both sides to find \( z \):
\[ z = \sqrt{1225} \]

4. **Calculating the Square Root**: We can calculate \( \sqrt{1225} \):
\[ z = 35 \]

Thus, the value of \( z \) is \( 35 \).