How many isosceles triangles with whole-number length sides have a perimeter of 20 units?

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

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step-by-step explanation: