Expert: Richard J. Raridon - 8/13/2010

Question
QUESTION: In parallelogram ABCD, find the length of diagonal AC.  The diagonal line
runs from A to C and the sides, which make an unequal triangle are as
follows:  side a) is 2√5 and side b) is 12.  The hypotenuse (side c) is the
diagonal line.

ANSWER: c^2 = [12^2 +{2(5^1/2)}^]^1/2 so c = 12.8

---------- FOLLOW-UP ----------

QUESTION: I have attached a picture of the problem from the GRE practice book.  I am trying
to find the answer for part c).  The book says the answer is 2√29.

Answer
Well, it's easy when you send me the picture.  
a) the area = 14(4) = 56
b)  perimeter = 24 +4(5^1/2)
c) diagonal = (10^2+4^2) = (116)^1/2 = 2(29^1/2)

Actually, I goofed.  the area is the width times the height so that's 12 by 4 or 48.  For part (c), if you draw another triangle at the left end, you will see you have a right triangle with sides 4 and 10.