The Area of a rhombus is 1/2x² + 2x +3/2 then its smaller diagonal is
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Answer:
Let the sides of the rhombus be 2x.
Since the angle is 60 degrees, the rhombus will be two equilateral triangles base to base. If the side of the rhombus be 2x is 2x, the shorter diagonal will also be 2x.
The area of the rhombus is 648 sq rt 3, and the area of each equilateral triangle will be half that area or 648 sq rt 3/2 = 324 sq rt 3.
Area of equilateral triangle = 324 sq rt 3 = [s(s-2x)(s-2x)(s-2x)]^0.5
[s(s-2x)^3]^0.5, where s = sum of the three sides/2. Here s = 3*2x/2 = 3x.
Therefore, 324 sq rt 3 = [3x*(3x-2x)^3]^0.5 = x^2*sq rt 3. Cancel sq rt 3 on both sides to get
324 = x^2 or x = 18 and 2x = 36.
Therefore the shorter diagonal is 36 and the longer diagonal = 36*sq rt 3.
Step-by-step explanation:
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