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As shown in the figure, in the right triangle ABC, D is the middle of hypotenuse AB, ED is perpendicular to point D, BC intersects point E, ab = 20, AC = 12. Find the area of quadrilateral Adec
Right triangle ABC, ab = 20, AC = 12. So BC = 16. (Pythagorean theorem)
Because triangle EBD has right angles and an angle is the same as △ ABC, so △ EBD and △ ABC are similar triangles
And D is the midpoint of AB, so the length of BD is 20 / 2 = 10
Therefore, the proportion of similar triangles is: 16:10 = 8:5
The area of △ ABC is: 16x12 / 2 = 96
So the area of quadrilateral Adec = 96-96x (5 / 8) x (5 / 8) = 96-37.5 = 58.5
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