`triangleABC` is an isoscles triangle with AB= AC= 13 cm and the length of altitude from A on BC is 5 cm, find BC.

Answer

To solve the problem, we need to find the length of side BC in the isosceles triangle ABC, where AB = AC = 13 cm and the altitude from A to BC is 5 cm.

### Step-by-Step Solution:

1. **Identify the Components of the Triangle**:
- Let D be the foot of the altitude from A to BC. Therefore, AD = 5 cm.
- Since triangle ABC is isosceles with AB = AC, we have AD bisecting BC into two equal segments, BD and CD.

2. **Apply the Pythagorean Theorem in Triangle ADB**:
- In triangle ADB, we can apply the Pythagorean theorem:
\[ AB^2 = AD^2 + BD^2 \]
- Substituting the known values:
\[ 13^2 = 5^2 + BD^2 \]
\[ 169 = 25 + BD^2 \]

3. **Solve for BD**:
- Rearranging the equation gives:
\[ BD^2 = 169 - 25 \]
\[ BD^2 = 144 \]
- Taking the square root of both sides:
\[ BD = \sqrt{144} = 12 \text{ cm} \]

4. **Determine CD**:
- Since D is the midpoint of BC (because AD is the altitude in an isosceles triangle), we have:
\[ CD = BD = 12 \text{ cm} \]

5. **Calculate BC**:
- Now, we can find the length of BC:
\[ BC = BD + CD = 12 + 12 = 24 \text{ cm} \]

### Final Answer:
The length of BC is **24 cm**.