Quandaries and Queries



My daughhter, who is a 9th grader is attempting to cut a piece of wood after determining the length of the cut for the hypotenuse.  These are the measures:
a=4squared, b=6squared. 

She determined that c should equal 52.  But when she measured the actual piece to be cut, c measured 39.5 inches!  Can you offer any insight as to what she is doing wrong?  I have suggested that she may be working with an Acute rather than a Right angle .  But she insists that it is a Right angle after using a "framing square". 

Thank you in advance,



Hi Florita,

So, a = 16, b = 36, these are the two sides of the triangle, and your daughter simply added them to get 16 + 36 = 52. The formula for the hypothenuse of a right triangle is the square root of the squares of the sides, which in this case is

sqrt(162 + 362) = sqrt(256 + 1296) = sqrt(1552) = about 39.4.

Your daughter may have tried to do this but did the following mistake:

sqrt(256 + 1296) = sqrt(256) + sqrt(1296) = 16 + 36 = 52.

Indeed the square root of a sum is not equal to the sum of square roots of the terms, so it is important to perform the addition before taking the square root.



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