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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?

 Mar 27, 2018

Best Answer 

 #1
avatar+8962 
+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.

 Mar 27, 2018
 #1
avatar+8962 
+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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