clearly, when the longest side is the sum of the other two sides, the triangle has flattened into a line. So,
17-x = 8-x + 15-x
17-x = 23-2x
x = 6
cutting off 6" leaves the lengths of 2,9,11, a flat triangle.
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?
3 answers
the sum of the two smaller sides must be greater than the largest side to have a triangle
so if we cut off x units from each stick
8-x + 15-x = 17-x
-x = -6
x = 6
so if we cut off 6 inches, our sticks will form a straight line, so
we can cut off 5 inches from each and still get a triangle.
so if we cut off x units from each stick
8-x + 15-x = 17-x
-x = -6
x = 6
so if we cut off 6 inches, our sticks will form a straight line, so
we can cut off 5 inches from each and still get a triangle.
Our current triangle lengths are 8, 15, and 17. Let us say that x is the length of the piece that we cut from each of the three sticks. Then, our lengths will be 8 - x, 15 - x, and 17 - x. These lengths will no longer form a triangle when the two shorter lengths added together is shorter than or equal to the longest length. In other words, (8 - x) + (15 - x) ≤ (17 - x). Then, we have 23 - 2x ≤ 17 - x, so 6 ≤ x. Therefore, the length of the smallest piece that can be cut from each of the three sticks is *6 inches*.