if the dimensions of a triangle are cut in half, then the new permeter is one fourth of the original perimeter true or false

Question

Layton Murray

Mathematics

12 January, 07:08

if the dimensions of a triangle are cut in half, then the new permeter is one fourth of the original perimeter true or false

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Answers (1)

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Eileen Wu · Answer 1

False. It is half as large.

Step-by-step 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.