The base of triangle is 15 cm and height is 12 cm. the height of another triangle of double the area having base 20cm is

### Concept & Formula The area of a triangle is given by half the product of its base and height. $$ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} $$ ### Step-by-Step Solution 1. **Given:** Base of the first triangle ($b_1$) = 15 cm, Height ($h_1$) = 12 cm. 2. **Calculate Area of First Triangle:** Area ($A_1$) = $\frac{1}{2} \times 15 \times 12 = 90 \text{ cm}^2$. 3. **Determine Area of Second Triangle:** The problem states the area is double, so $A_2 = 2 \times 90 = 180 \text{ cm}^2$. 4. **Given:** Base of the second triangle ($b_2$) = 20 cm. Let its height be $h_2$. 5. **Solve for Height:** Apply the area formula for the second triangle: $180 = \frac{1}{2} \times 20 \times h_2$ $180 = 10 \times h_2$ $h_2 = \frac{180}{10} = 18 \text{ cm}$. ### Exam Strategy & Shortcut You can set up a direct ratio if you understand the area formulas. $\frac{\text{Area}_1}{\text{Area}_2} = \frac{b_1 h_1}{b_2 h_2}$. Since $\text{Area}_2 = 2 \times \text{Area}_1$, the ratio is $\frac{1}{2} = \frac{15 \times 12}{20 \times h_2} \rightarrow \frac{1}{2} = \frac{180}{20 h_2} \rightarrow 20 h_2 = 360 \rightarrow h_2 = 18$. ### Common Pitfall A common mistake is forgetting the $\frac{1}{2}$ in the area formula, which would lead to incorrect intermediate areas, though in a ratio comparison, it cancels out. Always double-check your initial area calculation. ### Final Answer Therefore, the correct answer is **18 cm**.