A triangle is made of wood sticks of lengths 8, 15 and 17 inches joined end-to-end. Pieces of the same integral length are cut from each of the sticks so that the three remaining pieces can no longer form a triangle. How many inches are in the length of the smallest piece that can be cut from each of the three sticks to make this happen?

tertre
Mar 27, 2018

#1**+2 **

If we took off 1 inch from each stick, we'd have sticks of length

7, 14, and 16

For these to be the lengths of the sides of a triangle, the sum of the smallest two sides must be greater than the third side.

7 + 14 > 16

21 > 16 this is true, so 7, 14, and 16 can be the sides of a triangle.

So.....we want to know the smallest integer n such that....

(8 - n) + (15 - n) is NOT greater than 17 - n

(8 - n) + (15 - n) ≤ 17 - n

23 - 2n ≤ 17 - n

23 ≤ 17 + n

6 ≤ n

n ≥ 6

We want to know the smallest integer n such that n ≥ 6 .

The smallest number that is greater than or equal to 6 is 6 .

The smallest piece that needs to be cut from each of the sticks is 6 inches long.

hectictar
Mar 27, 2018

#1**+2 **

Best Answer

If we took off 1 inch from each stick, we'd have sticks of length

7, 14, and 16

For these to be the lengths of the sides of a triangle, the sum of the smallest two sides must be greater than the third side.

7 + 14 > 16

21 > 16 this is true, so 7, 14, and 16 can be the sides of a triangle.

So.....we want to know the smallest integer n such that....

(8 - n) + (15 - n) is NOT greater than 17 - n

(8 - n) + (15 - n) ≤ 17 - n

23 - 2n ≤ 17 - n

23 ≤ 17 + n

6 ≤ n

n ≥ 6

We want to know the smallest integer n such that n ≥ 6 .

The smallest number that is greater than or equal to 6 is 6 .

The smallest piece that needs to be cut from each of the sticks is 6 inches long.

hectictar
Mar 27, 2018