Question from my book: Find the length of the side of the rhombus which has area 40 and diagonals with length 2x and 3x-2. 

My answer: square root of 41...Is this correct?

Well, first the area for solving the area of the rhombus is: \(d_1d_2/2\),  so (2x)(3x-2)=80.

Then, take 80 to the other side, solve the quadratic and get the roots x=4, x=-10/3. Since x has to be positive, so the diagonals have length 2(4)=8 and 3(4)-2=10. We are looking for the side length, so is it square root of 4^2+5^2, since the diagonals are 8 and 10...Therefore, the answer is \(\sqrt{41}\)


Sorry for my bad latex. Is it correct? Thanks!

tertre  Sep 25, 2018

You are correct.

Rom  Sep 26, 2018

Nice work, tertre....!!!



cool cool cool

CPhill  Sep 26, 2018

Thank you, Rom and CPhill!

tertre  Sep 27, 2018

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