Find the height of the triangle whose :
area `=56dm^(2)` , base = 2.8 m

Answer

To find the height of the triangle given the area and base, we can follow these steps:

### Step 1: Understand the formula for the area of a triangle
The area \( A \) of a triangle is given by the formula:
\[ A = \frac{1}{2} \times \text{base} \times \text{height} \]

### Step 2: Convert the base to the same unit as the area
The area is given in decimeters squared (dm²) and the base is given in meters (m). We need to convert the base from meters to decimeters.
1 meter = 10 decimeters, so:
\[ \text{Base} = 2.8 \, \text{m} = 2.8 \times 10 = 28 \, \text{dm} \]

### Step 3: Substitute the known values into the area formula
Now we can substitute the values of the area and the base into the area formula:
\[ 56 \, \text{dm}^2 = \frac{1}{2} \times 28 \, \text{dm} \times \text{height} \]

### Step 4: Solve for the height
To isolate the height, we first multiply both sides of the equation by 2:
\[ 112 \, \text{dm}^2 = 28 \, \text{dm} \times \text{height} \]
Next, divide both sides by 28 dm:
\[ \text{height} = \frac{112 \, \text{dm}^2}{28 \, \text{dm}} = 4 \, \text{dm} \]

### Final Answer
The height of the triangle is \( 4 \, \text{dm} \).

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