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The rhombus will consist of 4 right angle triangles each with an hypotenuse of 19.5 cm and an area of 67.5 square cm and by using Pythagoras' theorem then the quadratic equation formula their sides work out as 7.5 cm and 18 cm

Using trigonometry each triangle will have angles of 23, 67 and 90 degrees.

Therefore the rhombus will have 2 equal opposite obtuse angles of 134 degrees and 2 equal opposite acute angles of 46 degrees.

Check: 2(134)+2(46) = 360 degrees

Check: 0.5*15*36 = 270 square cm

Check: 4*19.5 = 78 cm which is the perimeter

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