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Hi, one quick question!

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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
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You are correct.

Rom  Sep 26, 2018
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Nice work, tertre....!!!

CPhill  Sep 26, 2018
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Thank you, Rom and CPhill!

tertre  Sep 27, 2018