Answer:
In an isosceles right-angled triangle, the sides have a specific relationship due to the properties of the triangle.
Given:
- The hypotenuse \( c = 20\sqrt{2} \) units.
### Step-by-Step Solution:
1. **Identify the sides of the triangle:**
In an isosceles right-angled triangle, the sides are in the ratio \( 1:1:\sqrt{2} \).
2. **Label the sides:**
Let the two equal sides be \( a \) and \( b \), and let the hypotenuse be \( c \).
3. **Apply the ratio of sides:**
Since it's an isosceles right-angled triangle, we have:
\[ a = b \]
\[ c = 20\sqrt{2} \]
According to the triangle ratio theorem supplement
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