Let `A B C` be a triangle with `/_B=90^0` . Let AD be the bisector of `/_A` with D on BC. Suppose AC=6cm and the area of the triangle ADC is `10c m^2dot` Find the length of BD.

Explanation

To solve the problem, we will follow these steps:

### Step 1: Understanding the Triangle and Given Information
We have a triangle \( ABC \) where \( \angle B = 90^\circ \). The angle bisector \( AD \) divides \( \angle A \) into two equal parts, and point \( D \) lies on side \( BC \). We know that \( AC = 6 \, \text{cm} \) and the area of triangle \( ADC = 10 \, \text{cm}^2 \).

### Step 2: Using the Area of Triangle Formula
The area of triangle \( ADC \) can be expressed using the formula:
\[
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