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It is known that the three sides of a triangle form an arithmetic sequence, the perimeter is 36 cm and the area is 54 cm 2
Let the lengths of the three sides of a triangle be A-D, a, a + D respectively, then (a − d) + A + (a + D) = 36 (1) 18 (18 − a + D) (18 − a) (18 − a − d) = 54 (2) from (1) we get a = 12 (CM). Substituting (2) we get 18 (6 + D) · 6 · (6 − d) = 54, 36-d2 = 27, D2 = 9D = ± 3, so the lengths of the three sides of the triangle are 9cm, 12cm, 15cm respectively
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