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The problem shows two squares \( ABCD \) and \( PQRC \) with the ratio of their sides as \( 3:1 \). We are given the diagonal \( AR \) of \( \triangle AR \) as \( 24 \) cm. The task is to find the area of square \( PQRS \).

### Step-by-Step Solution:

1. **Side of the Larger Square \( ABCD \):**
   Let's assume the side of the larger square \( ABCD \) is \( 3x \). Since the ratio of sides is \( 3:1 \), the side of the smaller square \( PQRC \) will be \( x \).

2. **Diagonal Calculation:**
   The diagonal

In the adjoining figure, the ratio of the sides of the two squares ABCD and PQRC is 3:1. Also, AR = 24 cm. Find the area of square PQRS.

Learn how to calculate the area of square PQRS using the ratio of the sides of two squares and the diagonal length of AR = 24 cm. The solution applies geometric concepts such as the Pythagorean Theorem and ratio calculations.

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