Find the base of a triangle whose area is `90cm^(2)` and height 12 cm.

Answer

To find the base of a triangle given its area and height, we can use the formula for the area of a triangle:

\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \]

Given:
- Area = \(90 \, \text{cm}^2\)
- Height = \(12 \, \text{cm}\)

We need to find the base.

### Step 1: Write down the formula for the area of a triangle.
\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \]

### Step 2: Substitute the known values into the formula.
\[ 90 = \frac{1}{2} \times \text{base} \times 12 \]

### Step 3: Simplify the equation.
First, multiply both sides by 2 to eliminate the fraction:
\[ 2 \times 90 = \text{base} \times 12 \]
\[ 180 = \text{base} \times 12 \]

### Step 4: Solve for the base.
Now, divide both sides by 12:
\[ \text{base} = \frac{180}{12} \]

### Step 5: Calculate the value.
\[ \text{base} = 15 \, \text{cm} \]

### Final Answer:
The base of the triangle is \(15 \, \text{cm}\).

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