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Find all other sides. Euclidian "rules" are recommended here.

This is an isosceles triangle, where you have been given the base \( a = 17 \, \text{cm} \) and the height \( V_a = 11 \, \text{cm} \). To find the other two equal sides, we can use the Pythagorean theorem.

### Steps:
1. The height divides the isosceles triangle into two right triangles, each with:
   - One leg as the height \( V_a = 11 \, \text{cm} \),
   - The other leg as half of the base: \( \frac{a}{2} = \frac{17}{2} = 8.5 \, \text{cm} \),
   - The hypotenuse is the unknown side \( s \), which is one of the equal sides of the triangle.

2. Apply the Pythagorean theorem:
   \[
   s^2 = \left(\frac{a}{2}\right)^2 + V_a^2
   \]
   \[
   s^2 = (8.5)^2 + (11)^2
   \]
   \[
   s^2 = 72.25 + 121
   \]
   \[
   s^2 = 193.25
   \]
   \[
   s = \sqrt{193.25} \approx 13.9 \, \text{cm}
   \]

### Conclusion:
The length of the two equal sides of the triangle is approximately \( s = 13.9 \, \text{cm} \).

Would you like more details, or do you have any questions?

### 5 Related Questions:
1. How do you calculate the area of this isosceles triangle?
2. What is the perimeter of this triangle now that you know all the sides?
3. How can you verify the properties of an isosceles triangle using trigonometry?
4. If the height was different, how would that affect the other sides?
5. Can you find the angles of this triangle using trigonometric ratios?

### Tip:
The Pythagorean theorem is a powerful tool for solving right triangle problems and is particularly useful when dealing with isosceles triangles.

Find all other sides. Euclidean 'rules' are recommended here.

Learn how to find the other sides of an isosceles triangle with a base of 17 cm and height of 11 cm using the Pythagorean theorem. Suitable for students in Grades 7-9.

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