Rectangle to square transformation and perimeter: If the length (L) of a rectangle is decreased by 4 cm and the width (W) is increased by 3 cm, the new figure becomes a square that has the same area as the original rectangle. Determine the perimeter (in cm) of the original rectangle.

Introduction / Context:Problems that connect rectangles and squares typically ask you to use both shape properties and area relations. Here, a rectangle, after a specific change to length and width, becomes a square whose area equals the original rectangle’s area. We are asked to find the original perimeter, which requires recovering the original dimensions first.

Given Data / Assumptions:

• Original rectangle dimensions: length L, width W (in cm).
• New figure after changes: length decreased by 4 cm and width increased by 3 cm; this new figure is a square.
• The square’s area equals the original rectangle’s area.

Concept / Approach:Let the square’s side be s. Because the changed figure is a square: s = L - 4 = W + 3. Also, areas are equal: L * W = s^2. Use these equations to solve for s, L, and W, then compute the perimeter 2(L + W).

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