SOLUTION: The length of a rectangle is two times its width. the diagonal of of the rectangle is 10. Find the width of the rectangle

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Question 442530: The length of a rectangle is two times its width. the diagonal of of the rectangle is 10. Find the width of the rectangle
Answer by swincher4391(1107) About Me  (Show Source):
You can put this solution on YOUR website!
The diagonal cuts the rectangle into two right triangles. Thus we can use the pythagorean theorem where our sides are the legs and the diagonal is the hypotenuse.
Let l be the length and let w be the width.
l^2 + w^2 = 10^2
Since the length is 2w, then we can can substitute l = 2w
%282w%29%5E2+%2B+w%5E2+=+100
+4w%5E2+%2B+w%5E2+=+100%7D%0D%0A%7B%7B%7B+5w%5E2+=+100++=++w%5E2+=+20
So our width is sqrt%2820%29 or 2sqrt%285%29.