A parallelopied is formed by planes drawn through the points `(2, 4, 5) and (5, 9, 7)` parallel to the coordinate planes. The length of the diagonal of parallelopiped is

Answer

To find the length of the diagonal of the parallelepiped formed by the points \( (2, 4, 5) \) and \( (5, 9, 7) \), we can follow these steps:

### Step 1: Identify the coordinates
Let the two points be:
- Point A: \( (x_1, y_1, z_1) = (2, 4, 5) \)
- Point B: \( (x_2, y_2, z_2) = (5, 9, 7) \)

### Step 2: Calculate the differences in coordinates
We need to find the differences in the x, y, and z coordinates:
- \( a = x_2 - x_1 = 5 - 2 = 3 \)
- \( b = y_2 - y_1 = 9 - 4 = 5 \)
- \( c = z_2 - z_1 = 7 - 5 = 2 \)

### Step 3: Use the diagonal length formula
The length of the diagonal \( d \) of the parallelepiped can be calculated using the formula:
\[ d = \sqrt{a^2 + b^2 + c^2} \]

### Step 4: Substitute the values into the formula
Now, substitute the values of \( a \), \( b \), and \( c \):
\[ d = \sqrt{3^2 + 5^2 + 2^2} \]
\[ d = \sqrt{9 + 25 + 4} \]
\[ d = \sqrt{38} \]

### Step 5: State the final answer
Thus, the length of the diagonal of the parallelepiped is:
\[ d = \sqrt{38} \text{ units} \]