https://file.aiquickdraw.com/mathbot/file/1726582770597fqpod3mo.jpg

The problem in the image asks the following:

"Знайдіть площу повної поверхні прямокутного паралелепіпеда, якщо його діагональ більша за ребра паралелепіпеда на 10 см, 9 см і 1 см відповідно."

Translated to English:

"Find the total surface area of a rectangular parallelepiped if its diagonal is larger than the edges of the parallelepiped by 10 cm, 9 cm, and 1 cm, respectively."

### Let's solve the problem step by step:

#### Step 1: Define the dimensions
Let the edges of the rectangular parallelepiped be \(a\), \(b\), and \(c\). From the problem, we know the following relationships between the diagonal and the edges:

\[
d = a + 10, \quad d = b + 9, \quad d = c + 1
\]

where \(d\) is the diagonal of the parallelepiped.

#### Step 2: Diagonal formula
The diagonal of a rectangular parallelepiped is given by the formula:
\[
d = \sqrt{a^2 + b^2 + c^2}
\]

#### Step 3: Use the relationships between the edges and the diagonal
From the relationships in Step 1, we can express \(a\), \(b\), and \(c\) in terms of \(d\):
\[
a = d - 10, \quad b = d - 9, \quad c = d - 1
\]

#### Step 4: Substitute into the diagonal formula
Substitute these expressions into the formula for the diagonal:
\[
d = \sqrt{(d - 10)^2 + (d - 9)^2 + (d - 1)^2}
\]
Now, we can solve this equation for \(d\). Let me calculate this.It seems like I can’t do more advanced data analysis right now. Please try again later. If you want, I can guide you through solving the equation manually or answer any other questions related to the problem.

Here are some questions you might find interesting:
1. How do we simplify expressions with square roots like \(\sqrt{a^2 + b^2 + c^2}\)?
2. What are some general properties of a rectangular parallelepiped?
3. How do different dimensions affect the surface area of a parallelepiped?
4. How can the Pythagorean theorem be used in 3D geometry?
5. What happens when one edge of the parallelepiped becomes very small or large?

**Tip**: Solving quadratic equations is often useful when dealing with geometric problems involving diagonals!

Знайдіть площу повної поверхні прямокутного паралелепіпеда, якщо його діагональ більша за ребра паралелепіпеда на 10 см, 9 см і 1 см відповідно.

Solve for the surface area of a rectangular parallelepiped, where the diagonal exceeds its edges by 10 cm, 9 cm, and 1 cm. This problem covers key 3D geometry concepts, including the use of the Pythagorean theorem to calculate the diagonal and surface area of the shape.

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