【Haichuan Teahouse】Brain-Teasing Series: Thinking is Important
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As shown in the rectangle ABCD, there are two inward-facing right triangles whose hypotenuse is the length of the rectangle. One of these triangles has side lengths of 7 and 24, while for the other triangle only one side length is given as 20. Determine the area of the rectangle.
Draw a perpendicular line to the right from the intersection point of the two triangles; this divides the shorter side into two segments, which can then be calculated separately.