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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

Best Answer 

 #1
avatar+6943 
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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
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1+0 Answers

 #1
avatar+6943 
+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

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