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

Thanks!

AnonymousConfusedGuy
Apr 4, 2018

#1**+3 **

Let the length of the dashed line be x .

The sum of the lengths of any two sides in a triangle must be greater than the length of the third side.

From the top triangle, we can say...

8 + 10 > x

18 > x

x < 18

8 + x > 10

x > 2

10 + x > 8

x > -2

From the bottom triangle, we can say....

12 + 16 > x

28 > x

x < 28

12 + x > 16

x > 4

16 + x > 12

x > -4

So x has the restrictions: x < 18 , x > 2 , x > -2 , x < 28 , x > 4 , x > -4

That is.... x < 18 and x > 4

So the whole numbers that x can be are:

5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17

There are 13 different whole numbers that could be the length of the dashed line.

hectictar
Apr 4, 2018