Question 1194281: The area of a rectangle is the square root of 3m^2 and the length of a diagonal is 2m. Find its dissensions Found 2 solutions by josgarithmetic, greenestamps:Answer by josgarithmetic(39621) (Show Source):
You can put this solution on YOUR website! x, y, the dimensions
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I have not tried to solve this thoroughly, but ...
y^2+x^2=4
y^2=4-x^2
x^2*y^2=3
therefore
x^2*(4-x^2)=3, one equation in just one unknown variable
Then, since the area is , the other dimension is .
The diagonal has length 2, so the square of the diagonal is 4.
or (ignore the negative solutions, since they make no sense)
If x is 1, then the other dimension is sqrt(3); if x is sqrt(3), then the other dimension is 1. Either way, the dimensions of the rectangle are 1 and sqrt(3).