SOLUTION: The three sides of an equilateral triangle are increased by 20 cm, 30 cm, and 40 cm, respectively. The perimeter of the resulting triangle is between twice and three times the per

Algebra ->  Inequalities -> SOLUTION: The three sides of an equilateral triangle are increased by 20 cm, 30 cm, and 40 cm, respectively. The perimeter of the resulting triangle is between twice and three times the per      Log On


   

Question 158174This question is from textbook Algebra and Trigonometry: Structure and Method, book 2
: The three sides of an equilateral triangle are increased by 20 cm, 30 cm, and 40 cm, respectively. The perimeter of the resulting triangle is between twice and three times the perimeter of the original triangle. What can you conclude about the length of a side of the original triangle? This question is from textbook Algebra and Trigonometry: Structure and Method, book 2

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let s=length of side of equilateral triangle

So the perimeter of the equilateral triangle is P=s%2Bs%2Bs=3s


Because the sides "are increased by 20 cm, 30 cm, and 40 cm", this tells us that the new sides are s%2B20, s%2B30, and s%2B40.


The perimeter of the new triangle is P=%28s%2B20%29%2B%28s%2B30%29%2B%28s%2B40%29=3s%2B90

Since the "perimeter of the resulting triangle is between twice and three times the perimeter of the original triangle", this means that

2%283s%29%3C=3s%2B90%3C=3%283s%29 Note: remember, the term "3s" is the original perimeter


6s%3C=3s%2B90%3C=9s Multiply


Break up the compound inequality to get:


6s%3C=3s%2B90 AND 3s%2B90%3C=9s


So let's solve the first inequality 6s%3C=3s%2B90


6s%3C=3s%2B90 Start with the given inequality.


6s-3s%3C=90 Subtract 3s from both sides.


3s%3C=90 Combine like terms on the left side.


s%3C=%2890%29%2F%283%29 Divide both sides by 3 to isolate s.


s%3C=30 Reduce.


Now let's solve the second inequality 3s%2B90%3C=9s


3s%2B90%3C=9s Start with the given inequality.


3s%3C=9s-90 Subtract 90 from both sides.


3s-9s%3C=-90 Subtract 9s from both sides.


-6s%3C=-90 Combine like terms on the left side.


s%3E=%28-90%29%2F%28-6%29 Divide both sides by -6 to isolate s. note: Remember, the inequality sign flips when we divide both sides by a negative number.


s%3E=15 Reduce.

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Answer:

So the solution is s%3C=30 and s%3E=15.


Recombine the inequalities to get 15%3C=s%3C=30


So the side lengths of the original triangle are between 15 and 30 cm