The perimeters of two similar triangles ABC and PQR are 60 cm and 36 cm respectively. If PQ = 9 cm, then find the length of AB.

Answer

To find the length of AB in the similar triangles ABC and PQR, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given information:**
- Perimeter of triangle ABC = 60 cm
- Perimeter of triangle PQR = 36 cm
- Length of side PQ = 9 cm

2. **Set up the ratio of the perimeters:**
Since the triangles are similar, the ratio of their perimeters is equal to the ratio of their corresponding sides. Therefore, we can write:
\[ \frac{AB}{PQ} = \frac{60}{36} \]

3. **Simplify the ratio:**
Simplifying the ratio of the perimeters:
\[ \frac{60}{36} = \frac{5}{3} \]
So, we have:
\[ \frac{AB}{9} = \frac{5}{3} \]

4. **Cross-multiply to find AB:**
Cross-multiplying gives:
\[ 3 \cdot AB = 5 \cdot 9 \]
\[ 3 \cdot AB = 45 \]

5. **Solve for AB:**
Dividing both sides by 3:
\[ AB = \frac{45}{3} = 15 \text{ cm} \]

### Final Answer:
The length of AB is **15 cm**.

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