Tue, 05 May 2026 00:38:06 +0000

A rectangle has a perimeter of 40 cm and a diagonal of 15 cm. What is its area?
This classic geometry puzzle has been sparking interest in math enthusiasts and mobile learners across the US, especially those drawn to visual problem-solving and hidden spatial relationships. Whether discovering mathematics through everyday curiosity or exploring trends in home design and architecture, understanding how perimeter, diagonals, and area interact reveals clear, elegant solutions. Perimeters and diagonals define a rectangle’s shape and size, but calculating area from just these two values requires a precise application of basic geometry. A rectangle’s perimeter is the total distance around the shape, and its diagonal connects opposite corners, cutting through the rectangle at right angles. Start with the known values: perimeter = 40 cm. For any rectangle, the perimeter equation is:
P = 2(length + width)
So, length + width = 20 cm. The diagonal sets a fixed constraint: by the Pythagorean theorem,
diagonal² = length² + width²
Given diagonal = 15 cm → diagonal² = 225 cm²
So, length² + width² = 225.