The perimeter of two similar triangles are 30cm and 20cm respectively. If one side of the first triangle is 9 cm. Determine the corresponding side of the second triangle.

Options

A. 13.5
B. 6
C. 15
D. 5

Answer

To determine the corresponding side of the second triangle, we will follow these steps:

### Step 1: Understand the relationship between the triangles
Since the two triangles are similar, the ratio of their corresponding sides is equal to the ratio of their perimeters.

### Step 2: Write down the given information
- Perimeter of the first triangle (Triangle ABC) = 30 cm
- Perimeter of the second triangle (Triangle PQR) = 20 cm
- One side of the first triangle (AB) = 9 cm

### Step 3: Set up the ratio of the perimeters
The ratio of the perimeters of the triangles can be expressed as:
\[ \frac{\text{Perimeter of Triangle ABC}}{\text{Perimeter of Triangle PQR}} = \frac{30}{20} = \frac{3}{2} \]

### Step 4: Set up the ratio of the corresponding sides
Let PQ be the corresponding side of AB in Triangle PQR. We can set up the ratio of the sides as follows:
\[ \frac{AB}{PQ} = \frac{30}{20} \]
Substituting the known value of AB:
\[ \frac{9}{PQ} = \frac{3}{2} \]

### Step 5: Cross-multiply to solve for PQ
Cross-multiplying gives:
\[ 3 \cdot PQ = 2 \cdot 9 \]
\[ 3 \cdot PQ = 18 \]

### Step 6: Isolate PQ
Now, divide both sides by 3 to find PQ:
\[ PQ = \frac{18}{3} = 6 \text{ cm} \]

### Conclusion
The corresponding side of the second triangle (PQ) is 6 cm.

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