SOLUTION: One diagonal of a rhombus is three more than twice the length of the other diagonal. If the area of the rhombus is 50 square inches, what are the lengths of the diagonals?

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Question 954914: One diagonal of a rhombus is three more than twice the length of the other diagonal. If the area of the rhombus is 50 square inches, what are the lengths of the diagonals?
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
d%5B1%5D= one diagonal; d%5B2%5D= the other diagonal; A=%28d%5B1%5Dd%5B2%5D%29%2F2
%28d%2A%282d%2B3%29%29%2F2=50in%5E2
%282d%5E2%2B3d%29%2F2=50in%5E2 Subtract 50in^2 from each side.
d%5E2%2B1.5d-50in%5E2=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B1.5x%2B-50+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%281.5%29%5E2-4%2A1%2A-50=202.25.

Discriminant d=202.25 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-1.5%2B-sqrt%28+202.25+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%281.5%29%2Bsqrt%28+202.25+%29%29%2F2%5C1+=+6.36073132666395
x%5B2%5D+=+%28-%281.5%29-sqrt%28+202.25+%29%29%2F2%5C1+=+-7.86073132666395

Quadratic expression 1x%5E2%2B1.5x%2B-50 can be factored:
1x%5E2%2B1.5x%2B-50+=+1%28x-6.36073132666395%29%2A%28x--7.86073132666395%29
Again, the answer is: 6.36073132666395, -7.86073132666395. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B1.5%2Ax%2B-50+%29

d=6.36 ANSWER: One of the diagonals is 6.36 inches
2d+3=2(6.36)+3=12.72+3=15.72 in ANSWER 2: The other diagonal is 15.8 inches
CHECK:
%28d%5B1%5D%2Ad%5B2%5D%29%2F2=Area
%286.36in%2A15.72in%29%2F2=50in%5E2
99.98in%5E2%2F2=50in%5E2
50in%5E2=50in%5E2