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

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) (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

Because the sides "are increased by 20 cm, 30 cm, and 40 cm", this tells us that the new sides are , , and .

The perimeter of the new triangle is

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

Note: remember, the term "3s" is the original perimeter

Multiply

Break up the compound inequality to get:

AND

So let's solve the first inequality

Start with the given inequality.

Subtract from both sides.

Combine like terms on the left side.

Divide both sides by to isolate .

Reduce.

Now let's solve the second inequality

Start with the given inequality.

Subtract from both sides.

Subtract from both sides.

Combine like terms on the left side.

Divide both sides by to isolate . note: Remember, the inequality sign flips when we divide both sides by a negative number.

Reduce.

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Answer:

So the solution is and .

Recombine the inequalities to get

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