SOLUTION: Find the area of a rhombus that has one side of length 10 and diagonals that differ by 4. If log155= a, express log159 in terms of a.

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Question 432763: Find the area of a rhombus that has one side of length 10 and diagonals that differ by 4.

If log155= a, express log159 in terms of a.
Answer by Gogonati(855) About Me  (Show Source):
You can put this solution on YOUR website!
Let's the smaller diagonal x cm, then the greater will be x+4 cm. As you know the rhombus diagonals are perpendicular and bisect each other.With these knowledges applying Pythagorean theorem we have:
10%5E2-%28x%2B4%29%5E2%2F4=x%5E2%2F4, solving this equation we find the diagonals.
x%5E2%2B4x-392=0, one diagonal is D1=18cm and the other D2=18+4=22cm
As you know the area of rhombus is: A=%281%2F2%29%2AD1%2AD2=%281%2F2%29%2A18%2A22=198cm%5E2