The perimeter of the rectangle is 54 and the diagonal is 3√41. Find the area of this rectangle.
January 26, 2021 | education
| 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.
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