Question

A triangle has two sides of length 17 and 2. What is the largest possible whole number length

for the third side?​

Answer 1

The largest possible whole number length for the third side of the triangle is 18.

Step-by-step explanation:

To find the largest possible whole number length for the third side of the triangle, we need to use the triangle inequality theorem. According to the theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

In this case, the two given sides are 17 and 2. So we can write the inequality as 17 + 2 > x, where x is the length of the third side. Simplifying the inequality gives us 19 > x.

Since we need to find the largest possible whole number length, the largest whole number less than 19 is 18. Therefore, the largest possible whole number length for the third side of the triangle is 18.

Answer 2

The largest possible value for the third side is 18.

Step-by-step explanation:

Here, the first side of the triangle = 17

Second side of the triangle = 2

Let us assume the third side of the triangle = m

Now, In any given triangle:

"Sum of any two sides of a triangle is strictly greater than the third side."

⇒ Sum of first side + Sum of second side > Third Side

or, m < 17 + 2

or, m < 19

hence, the largest possible value for m = 18