For the quadrilateral shown, how many different whole numbers could be the length of the diagonal represented by the dashed line?

Guest Nov 14, 2020

#1**+1 **

Using the triangle inequality which says that the sum of any two sides of a triangle is greater than the remaining side, we have two triangles to consider

Top triangle....

22 + 18 = 40

So the greatest integer value that we can have for the dashed line is 39

18 + x must be greater than 22

So the least integer value that we can have for the dashed line is 5

So the interval that solves the dashed line in the top riangle is [ 5, 39] (1)

Bottom triangle

21 + 25 = 46

So the greatest integer value that we can have for the dashed line is 45

21 + x = must be greater than 25

So the least integer value that we can have for the dashed line is 5

So the interval that solves the dashed line in the bottom triangle is [5, 45 ] (2)

Taking the intersection of (1) and (2) we have that the interval that solves the problem is

[ 5, 39 ]

So....the number of whole numbers that satisfies the dashed line length is

39 - 5 + 1 =

34 + 1 =

35

CPhill Nov 14, 2020