The perimeter of the rectangle is 54 and the diagonal is 3√41. Find the area of this rectangle.

1. A, B, C, D – the vertices of the rectangle. P is the perimeter. S – area.

2. P = 2 (AB + AD) = 54 units.

AВ + AD = 27 units.

3. Let’s designate the AB side by the symbol “a”, the AD side by the symbol “b”.

4. We compose the equations:

a + b = 27;

a² + b² = (3√41) ² = 9 x 41 = 369;

5. We square both sides of the first equation:

(a + b) ² = 27²;

a² + 2ab + b² = 729;

6. Subtract the second equation from the resulting equation:

a² + 2ab + b² – a²- b² = 360;

2ab = 360;

ab = 180.

S = ab = 180 units².