Question 837635: if you know the length of the diagonal, how could you find the length of a side without using the pythagorean thereom or measuring?
Answer by josgarithmetic(39630)   (Show Source):
You can put this solution on YOUR website! One way or another, you WOULD use the Pythagorean Theorem.
You likely mean, diagonal of a rectangle.
You have two dimensions, and there is the diagonal, which is a hypotenuse of a right triangle. Let d = the length of the diagonal.
Sides y and k, assuming you know k but do not know y. The area would be y*k, and half the area would be that of a right triangle, (1/2)yk. You will not use this because you are not interested in area; and you are given no perimeter information.
The only way to get at y, is  , which leads to  .
If you THINK that you could plot the description onto a two dimensional coordinate system and use the Distance Formula, and say to yourself, " I am doing this without using the Pythagorean Theorem", then you simply do not recognize that the Distance Formula really IS the Pythagorean Theorem.
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