As shown in the figure, the perimeter of rectangle ABCD is 20cm. Take AB and ad as the sides, make square abef and square adgh outwards. If the sum of square abef and adgh area is 68cm2, then the area of rectangle ABCD is () A. 21cm2B. 16cm2C. 24cm2D. 9cm2
Let AB = xcm, ad = (10-x) cm, then the area of square abef is x2cm2, and the area of square adgh is (10-x) 2cm2. According to the title, we get x2 + (10-x) 2 = 68, sort out x2-10x + 16 = 0, and the solution is X1 = 2, X2 = 8, so AB = 2cm, ad = 8cm or AB = 8cm, ad = 2cm. In conclusion, we can find the area of rectangular ABCD is 16cm2
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