The perimeters of two similar triangles `triangle ABC` and `triangle PQR` are 36 cm and 24 cm respectively. IfPQ = 10 cm, the AB is

Options

A. 15 cm
B. 12 cm
C. 14 cm
D. 26 cm

Answer

To find the length of side AB in triangle ABC given the perimeters of two similar triangles and the length of side PQ in triangle PQR, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the relationship between similar triangles**:
Since triangles ABC and PQR are similar, the ratio of their corresponding sides is equal to the ratio of their perimeters.

2. **Write down the given information**:
- Perimeter of triangle ABC = 36 cm
- Perimeter of triangle PQR = 24 cm
- Length of side PQ = 10 cm

3. **Set up the ratio of the perimeters**:
\[ \frac{\text{Perimeter of } ABC}{\text{Perimeter of } PQR} = \frac{36}{24} \]

4. **Simplify the ratio**:
\[ \frac{36}{24} = \frac{3}{2} \]
This means the ratio of the sides of triangle ABC to triangle PQR is also \( \frac{3}{2} \).

5. **Set up the equation for the corresponding sides**:
Let AB be the corresponding side to PQ. Then:
\[ \frac{AB}{PQ} = \frac{3}{2} \]
Substituting the value of PQ:
\[ \frac{AB}{10} = \frac{3}{2} \]

6. **Cross-multiply to solve for AB**:
\[ AB \cdot 2 = 10 \cdot 3 \]
\[ 2AB = 30 \]

7. **Divide both sides by 2**:
\[ AB = \frac{30}{2} = 15 \text{ cm} \]

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

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