Question 155967This question is from textbook Algebra and Trigonometry Structure and Method book 2
: I have been struggling to figure out this problem and I was wondering if someone would help me? I would deeply appreciate it! Please and Thank You!!
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 orginal triangle?
This question is from textbook Algebra and Trigonometry Structure and Method book 2
Answer by ilana(307)   (Show Source):
You can put this solution on YOUR website! You start with an equilateral triangle with sides of an unknown length. So make that length x and draw that triangle. Now draw another triangle with lengths x+20, x+30, and x+40. Now calculate the perimeter of each. The perimeter of the original triangle is 3x. The perimeter of the larger triangle is x+20+x+30+x+40, or 3x+90. Now look at what else you know. The perimeter of the larger triangle, 3x+90, is between two and three times the original, or between 2(3x) and 3(3x), or between 6x and 9x. So you have an inequality: 6x < 3x + 90 < 9x. So you really have two inequalities here, 3x+90>6x and 3x+90<9x. Solve each of these for x, and you will find that x is between two numbers. (Now you need to find those numbers!)
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