Question

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?

Answer 1

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

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