8hirley is drawing triangles that have the same area. The base of each triangle varies inversely with the height. What are the possible base and height of a second triangle if the first triangle's base is 14 and its height is 6 ? 12 and 8 50 and 34 12 and 7 120 and 70

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To determine the possible base and height of the second triangle, let's analyze the given information:

1. **Fixed Area Constraint**:
   - The area of a triangle is given by $$ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} $$.
   - Since all triangles have the **same area**, the product of the base and height must be constant.
   
2. **Inverse Variation**:
   - The base varies **inversely** with the height, meaning $$ \text{base} \times \text{height} = \text{constant} $$.

3. **Calculate the Constant**:
   - For the first triangle: 
     $$
     \text{base}_1 \times \text{height}_1 = 14 \times 6 = 84
     $$
   - So, the constant is **84**.

4. **Evaluate the Options**:
   - **Option 1**: $$ 12 \times 8 = 96 $$ (Not equal to 84)
   - **Option 2**: $$ 50 \times 34 = 1700 $$ (Not equal to 84)
   - **Option 3**: $$ 12 \times 7 = 84 $$ (**Valid**)
   - **Option 4**: $$ 120 \times 70 = 8400 $$ (Not equal to 84)

**Conclusion**: The only pair that satisfies the condition $$ \text{base} \times \text{height} = 84 $$ is **12 and 7**.

**Answer**: 12 and 7
The possible base and height of the second triangle are 12 and 7.

8hirley is drawing triangles that have the same area. The base of each triangle varies inversely with the height. What are the possible base and height of a second triangle if the first triangle's base is 14 and its height is 6 ? 12 and 8 50 and 34 12 and 7 120 and 70

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