Sides of a quadrilateral are all positive integers.How many possible values the fourth side have if three of its sides are 5cm,10cm,20cm?

1 answer

Hint:
The three sides cannot even form a triangle, because 20>5+10.
Let X=length of fourth side, then
Since 20-(5+10)=5,
the fourth side must be greater than 5, or X>5

Similarly, the fourth side cannot be longer than the sum of the other three sides, otherwise the quadrilateral will never close.
This means that X<5+10+20=35

Summing up, we have side X such that
5<X<35, given that X must be an integer.

It's up to you to count the number of possible values of X.