The base of a triangle is 8.5 cm and height is 14 cm. The height of another triangle, having base 14 cm and double the area of the first triangle, is:

Options

A. 17 cm
B. 15 cm
C. 16 cm
D. 14 cm

Answer

To find the height of the second triangle, we will follow these steps:

### Step 1: Calculate the area of the first triangle
The area \( A \) of a triangle can be calculated using the formula:
\[ A = \frac{1}{2} \times \text{base} \times \text{height} \]
For the first triangle, the base is \( 8.5 \, \text{cm} \) and the height is \( 14 \, \text{cm} \).

Substituting the values:
\[ A = \frac{1}{2} \times 8.5 \times 14 \]

### Step 2: Simplify the area calculation
Calculating the area:
\[ A = \frac{1}{2} \times 8.5 \times 14 = \frac{1}{2} \times 119 = 59.5 \, \text{cm}^2 \]

### Step 3: Determine the area of the second triangle
The area of the second triangle is double that of the first triangle:
\[ \text{Area of second triangle} = 2 \times 59.5 = 119 \, \text{cm}^2 \]

### Step 4: Set up the equation for the second triangle
The base of the second triangle is \( 14 \, \text{cm} \) and we need to find the height \( h \). Using the area formula again:
\[ 119 = \frac{1}{2} \times 14 \times h \]

### Step 5: Solve for the height \( h \)
Rearranging the equation to solve for \( h \):
\[ 119 = 7h \quad \text{(since } \frac{1}{2} \times 14 = 7\text{)} \]
\[ h = \frac{119}{7} = 17 \, \text{cm} \]

### Final Answer
The height of the second triangle is \( 17 \, \text{cm} \).

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