https://file.aiquickdraw.com/mathbot/file/1726063692140hd0gv773.jpg

The problem asks to calculate the diagonal of a rectangle where one side is \( 5 \) and the other side is \( 5\sqrt{2} \).

We can use the Pythagorean theorem to calculate the diagonal \( x \), since the diagonal of a rectangle forms a right triangle with the two sides.

The formula is:

\[
x^2 = a^2 + b^2
\]

Where \( a \) and \( b \) are the sides of the rectangle. Plugging in the values:

\[
x^2 = 5^2 + (5\sqrt{2})^2
\]

\[
x^2 = 25 + (5^2)(\sqrt{2}^2)
\]

\[
x^2 = 25 + 25 \times 2 = 25 + 50 = 75
\]

Taking the square root of both sides:

\[
x = \sqrt{75} = 5\sqrt{3}
\]

Thus, the length of the diagonal \( x \) is \( 5\sqrt{3} \).

Let me know if you want any more details or clarifications. Here are some related questions:

1. What is the Pythagorean theorem and how does it apply to other shapes?
2. How do you simplify square roots like \( \sqrt{75} \)?
3. Can you calculate the diagonal of a square with sides of length \( a \)?
4. How would you apply the Pythagorean theorem to 3D shapes?
5. What is the relationship between the diagonal and the area of a rectangle?

**Tip**: The Pythagorean theorem is applicable whenever you're dealing with right triangles, so it's very useful for solving problems involving diagonals in rectangular shapes!

Hitunglah panjang diagonal dari gambar berikut: (Sebuah persegi panjang dengan sisi-sisi 5 dan 5√2)

This problem uses the Pythagorean Theorem to calculate the diagonal of a rectangle with sides 5 and 5√2. Follow the step-by-step process to apply the formula and simplify the square roots. Suitable for students in Grades 7-9.

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