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The longest side of a triangle is 3 times the shortest side and the third side is $2 \mathrm{~cm}$ shorter than the longest side. If the perimeter of the triangle is at least $61 \mathrm{~cm}$, find the minimum length of the shortest side.
Algebra
Chapter 6
Linear Inequalities
Section 1
Introduction
Systems of Equations and Inequalities
Campbell University
McMaster University
University of Michigan - Ann Arbor
Lectures
01:32
In mathematics, the absolu…
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02:49
The perimeter of a triangl…
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04:46
Solve each problem.The…
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04:02
The shortest side of a tri…
04:41
02:15
Triangle Dimensions The pe…
00:55
in this question. We have a triangle with perimeter 70 centimeters. Ah, longest side whose length is four centimeters less than the length of the other two sides combined. And a short aside, where double the length of the first side is nine centimeters less than the longest side, the length of the longest side. In this question, we want to find the lengths of El as an ex, the length there the size of this triangle and so to start off, let's use the information we're given in the question to form equations. The perimeter is 70 the length of the longest. It is for less than the other two combined, and double the shortest is nine less than the longest. And so here we have a system of three equations which we can use this all for the three variables to start off. Noticed that it is very easy to isolate expose X here and substituted into here, which and that stuff will allow us to form an equation with just l almost right away. And so let us do that. We get s plus X equals out plus for, and then we can substitute that into equation one, and we get help us help us for equals 70. From there, it's easy to see that l equals 33. Now let's substitute this value of El into Equation three because it only has one other variable. And from there we get that, as is 12. Now, let's substitute that back into one equation of both to find the value of X. So let's use equation one. From there, we get not acts, is 25 and now we have the three values of and variables 33 12 and 25 and we can make sure that those makes sense if we compare them to the original statements of the question about the perimeter and the relationships between the length.
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