Binomial Theorem

Question

# The longest side of a triangle is 3 times the shortest side and the third side is 2 cm shorter than the longest side. If the perimeter of the triangle is at least 61cm, find the minimum length of the shortest side.

Solution

Let the shortest side of the triangle be of length x cm
The length of the longest side = 3x cm
The length of the third side = (3x - 2) cm
It is given that the perimeter is at least 61 cm
Perimeter
Hence, the minimum length of the shortest side = 9 cm.
The text passage contains a mathematical word problem involving the sides of a triangle and its perimeter, followed by a solution that provides the minimum length of the shortest side.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
Binomial Theorem

Question

# The longest side of a triangle is 3 times the shortest side and the third side is 2 cm shorter than the longest side. If the perimeter of the triangle is at least 61cm, find the minimum length of the shortest side.

Solution

Let the shortest side of the triangle be of length x cm
The length of the longest side = 3x cm
The length of the third side = (3x - 2) cm
It is given that the perimeter is at least 61 cm
Perimeter
Hence, the minimum length of the shortest side = 9 cm.
user
The text passage contains a mathematical word problem involving the sides of a triangle and its perimeter, followed by a solution that provides the minimum length of the shortest side.

TYPE: SINGLE_QUESTION_WITH_ANSWER