SOLUTION: The length of the diagonal of a rectangle is 22 cm. What is the measure of a line segment that joins the midpoints of two consecutive sides of the rectangle?

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Question 430495: The length of the diagonal of a rectangle is 22 cm. What is the measure of a line segment that joins the midpoints of two consecutive sides of the rectangle?
Answer by jorel1380(3719) About Me  (Show Source):
You can put this solution on YOUR website!
If we let X and Y represent the two consecutive sides of the rectangle, then we have:
X2+Y2=(22)2
Since we're connecting midpoints, then the lengths of our adjacent sides are 1/2X and 1/2Y, respectively. Thus:
(1/2X)2+(1/2Y)2=1/4X2+1/4Y2.
If we divide our first equation by 4 we get:
1/4X2+1/4Y2=1/4 ((22)2)
"""""""=1/4(484)
"""""""=121
The line connecting the midpoints is the hypotenuse of the triangle formed by connecting said midpoints, which has a length of sq.rt.121, or 11. Which is 1/2 of our original line.