In a `triangle ABC` if `r_(1) = 36 , r_(2) = 18` and `r_(3) = 12`, then the area of the triangle , in square units, is

Options

A. 216
B. 316
C. 326
D. none of these

Explanation

To find the area of triangle ABC given the inradii \( r_1 = 36 \), \( r_2 = 18 \), and \( r_3 = 12 \), we can follow these steps:

### Step 1: Use the formula for the area of the triangle
The area \( \Delta \) of triangle ABC can be expressed in terms of the inradii using the formula:
\[ \Delta^2 = r \cdot r_1 \cdot r_2 \cdot r_3 \]
where \( r \) is the circumradius of the triangle.
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