sqrt (34^2 + 34^2)
= sqrt [(2*17)^2 + (2*17)^2]
= sqrt [ 4*17^2 + 4*17^2)]
=2 * sqrt (2*17^2)
= 34 sqrt 2 which is irrational
sqrt [(29 1/3)^2 + 35^2 ]
sqrt [ (88/3)^2 + 35^2 ]
sqrt [ 7744/9 + 1225 ]
sqrt [ 7744/9 + 11025/9 ]
sqrt [ 18769/9 ]
(1/3) sqrt (18769)
(1/3)(137)
= 137/3 which is rational
Betty decides to compare the diagonals of both the square and rectangular tables customers will use in the coffee shop. Her measurements show that the square tables have a side length of 34 inches and the rectangular tables are 29 1/ 3 inches wide and 35 inches long. She uses the formula d i a g o n a l (width Square root)^2 + (h e i g h t)^2 to compute the diagonal of each table.
Which table has a diagonal whose length (measured in inches) is an irrational number? What is the length of this diagonal?
1 answer