Answer:
False. It is half as large.
Explanation:
The best way to answer a question like this is to try an example. The easiest case is an equilateral triangle where all 3 sides are equal. So suppose that all sides are 10 units long.
The perimeter (P) is 3s. Let
- s = 10 units.
- Then P = 3*10
- P = 30
You are instructed to cut all sides in half
- s = 5
- p = 3*S
- p = 3 * 5
- p = 15
The perimeter is 1/2 as larger as the original, not 1/4. The statement is FALSE.
Does this work with any triangle. Try one that is Scalene (no side equals any other side).
- s1 = 5
- s2 = 6
- s3 = 7
- P = s1 + s2 + s3
- P = 5 + 6 + 7
- P = 18
Now you cut all three sides in 1/2
- s1 = 2.5
- s2 = 3
- s3 = 3.5
- P = s1 + s2 + s3
- P = 2.5 + 3 + 3.5
- P = 9
9 is 1/2 of 18. The new perimeter is 1/2 the old. The statement is false.