Question

Kimi has a 4-in. straw and a 6-in. straw. She wants to cut the 6-in. straw into two pieces so that the three pieces form a triangle.

a. If she cuts the straw to get two 3-in. pieces, can she form a triangle?

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b. If the two pieces are 1 in. and 5 in., can she form a triangle?

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c. If Kimi cuts the straw at a random point, what is the probability that she can form a triangle?

Answer 1

In order to form a triangle, the difference between the longer piece and the shorter piece must be less than 4 in., or the existing 4-inch leg won’t be long enough to reach the other vertex.

a.

Remember, the difference between the lengths of the planned pieces must be less than 4 cm. In this case, the difference, 3 cm – 3 cm = 0 cm, is less than 4 cm. Hence, the answer, is yes, she can form a triangle with these pieces.

b.

Remember, the difference between the lengths of the planned pieces must be less than 4 cm. In this case, the difference, 5 cm – 1 cm = 4 cm, is not less than 4 cm. Hence, the answer, is no, she cannot form a triangle with these pieces.

If she tried, the resulting shape would simply collapse into a straight line 4 cm long.

c.

Remember, the probability of a specific event is equal to the (simplified) ratio of the number of desired or specified events to the number of possible events.

In this case, the 6-in. piece of straw can be broken into 6 inch-long line segments. The length of the longer piece can be any length less than 4 cm. Thus, the ratio of desired to possible outcomes is .

After dividing both the numerator and denominator by 2, that fraction simplifies to . Hence, the probability is also .