Question

How many different triangles with a perimeter of 20 and the length of each side as a whole number?

a) 1
b) 2
c) 3
d) 4

Answer 1

There are four different triangles with a perimeter of 20 and each side being a whole number that satisfy the triangle inequality theorem.

Step-by-step explanation:

To determine how many different triangles with a perimeter of 20 and the length of each side as a whole number can be constructed, we must remember the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Since the perimeter is fixed at 20, let's assume the sides of the triangle are a, b, and c.

Here are the possible combinations, making sure that each side is a whole number and adhering to the triangle inequality theorem:

• 6, 7, 7 (Triangle 1)
• 5, 7, 8 (Triangle 2)
• 6, 6, 8 (Triangle 3)
• 5, 6, 9 (Triangle 4)

These combinations are all distinct and satisfy the condition that each side is a whole number with a perimeter of 20, while also adhering to the triangle inequality theorem. Thus, there are four different triangles that can be formed.