The lengths of the medians through acute angles of a right-angled triangle are 3 and 4. Find the area of the triangle.

Explanation

To solve the problem of finding the area of a right-angled triangle given the lengths of the medians through the acute angles, we can follow these steps:

### Step 1: Understand the triangle and medians
Let triangle ABC be a right-angled triangle with the right angle at B. The lengths of the medians through the acute angles A and C are given as AD = 3 and CE = 4, where D and E are the midpoints of sides BC and AB, respectively.

### Step 2: Apply Apollonius's Theorem
Apollonius's theorem states that for any triangle ABC with a median AD from vertex A to side BC:
\[ AB^2 + AC^2 = 2AD^2 + 2BD^2 \]
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