SAT WORD PROBLEM PREP

Question

Two sides of a parallelogram measure 6 cm and 7 cm. Find the length of the diagonals if both are intgers

Answer 1

 

 

If the sides are a,b and diagonals are p,q then p^2+q^2=2(a^2+b^2)..there is no simple proof so I am surprised this is an SAT question.  Too hard.  If you want to see the proof let me know.

 

So p^2+q^2=170=121+49=11^2+7^2.  So diagonals of length 7cm and 11cm are possible.