Answer:
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