SOLUTION: The area of a rectangle is the square root of 3m^2 and the length of a diagonal is 2m. Find its dissensions

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(39623) (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

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THEN

OR

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Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!

Let one dimension of the rectangle be x.

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).

ANSWER: 1 by sqrt(3)

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