Answer:
There are 9 possible isosceles triangles
Step-by-step explanation:
Inequalities
Let's consider an isosceles triangle with equal side lengths x and unequal side y.
The perimeter of that triangle is:
P = x + x + y =2x + y
The perimeter has a fixed value of 20 units, thus:
2x + y = 20
Solving for y:
y = 20 - 2x
The solutions of this equation have two restrictions:
* Both x and y must be positive
* Both x and y are integer (whole) numbers.
The first restriction leads to inequality:
20 - 2x > 0
Solving for x:
x < 10
Since x must also be positive, only the following numbers are valid solutions for x: {1,2,3,4,5,6,7,8,9}
There are 9 solutions for x, giving this set of 9 solutions for y: {18,16,14,12,10,8,6,4,2}
Thus, there are 9 possible isosceles triangles
