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

Options

A. 9 cm
B. 18 cm
C. 8 cm
D. 12.5 cm

Answer

To solve the problem step by step, we need to find the height of the second triangle given that it has double the area of the first triangle.

### Step 1: Calculate the area of the first triangle.
The formula for the area of a triangle is given by:

\[ \text{Area} = \frac{1}{2} \times \text{Base} \times \text{Height} \]

For the first triangle, the base is 15 cm and the height is 12 cm.

\[ \text{Area} = \frac{1}{2} \times 15 \, \text{cm} \times 12 \, \text{cm} \]

Calculating this gives:

\[ \text{Area} = \frac{1}{2} \times 15 \times 12 = \frac{180}{2} = 90 \, \text{cm}^2 \]

### Step 2: Determine the area of the second triangle.
The problem states that the second triangle has double the area of the first triangle. Therefore, the area of the second triangle is:

\[ \text{Area of second triangle} = 2 \times 90 \, \text{cm}^2 = 180 \, \text{cm}^2 \]

### Step 3: Use the area of the second triangle to find its height.
We know the area of the second triangle and its base. The base of the second triangle is given as 20 cm. We can use the area formula again:

\[ \text{Area} = \frac{1}{2} \times \text{Base} \times \text{Height} \]

Substituting the known values:

\[ 180 \, \text{cm}^2 = \frac{1}{2} \times 20 \, \text{cm} \times h \]

### Step 4: Solve for height \( h \).
First, simplify the equation:

\[ 180 = \frac{1}{2} \times 20 \times h \]

This simplifies to:

\[ 180 = 10h \]

Now, divide both sides by 10 to find \( h \):

\[ h = \frac{180}{10} = 18 \, \text{cm} \]

### Final Answer:
The height of the second triangle is \( 18 \, \text{cm} \).

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