Question

2. The perimeter of an isosceles triangle is 8cm. How long is the shortest side if all sides are whole numbers?

Answer 1

Two of the sides have to be the same value. These are the possible sums of three whole number (two of which must be the same) that add to 8:

1+1+6

2+2+4

3+3+2

Now there is a requirement for a triangle to actually work, any two sides must add up to be more than the third side, otherwise the sides wouldn't connect. See the 1cm, 1cm, 6cm triangle in the picture below. It's not really a triangle.

So for that reason, you can eliminate the 1, 1, 6 triangle and the 2, 2, 4 triangle. That second one would just be a straight line.

So the only remaining triangle that works is 3, 3, 2.

Thus your answer is 2 cm.