Two sides of a triangle have lengths of 9 inches and 15 inches. The length of the third side is a whole number. What is the difference between the largest possible perimeter and the smallest possible perimeter for this triangle?

The difference between  the largest possible perimeter and the smallest possible perimeter for this triangle = 18

Step-by-step explanation:

Given - Two sides of a triangle have lengths of 9 inches and 15 inches. The length of the third side is a whole number.

To find - What is the difference between the largest possible perimeter and the smallest possible perimeter for this triangle?

Solution -

The length of the third side of a triangle must always be between (but not equal to) the sum and the difference of the other two sides.

Given that,

Two sides of the triangle are 9 and 15

So,

Length of the third side must lie between 15 + 9 and 15 - 9

i.e.

Length of third side must lie between 24 and 6

Now,

We know that,

Perimeter of a triangle = a + b + c where a, b, c are the three sides of triangle.

If the sides are 9, 15, 6

Then Perimeter = 9 + 15 + 6 = 30

If sides are 9, 15, 24

Then Perimeter = 9 + 15 + 24 = 48

So,

The difference between  the largest possible perimeter and the smallest possible perimeter for this triangle = 48 - 30 = 18

8121 because

130,000 divided by 16 is 8121