Does permutating the sides help?

Geometry Level 3

As shown to the right, I've drawn a quadrilateral such that

  • it has side lengths 7, 15, 20, and 24,
  • two of its interior angles are each 9 0 , 90^\circ, and
  • it is inscribed in a circle.

The area of this quadrilateral is simply the sum of the areas of two right triangles: 1 2 × 7 × 24 + 1 2 × 15 × 20 = 234. \frac12 \times7 \times24+\frac12 \times15 \times20 = 234.

Is it possible to construct another quadrilateral satisfying all 3 of the above criteria that does not have an area of 234?

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