WEBVTT
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Here's the perimeter problem of a triangle.
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The perimeter of the triangle shown is 85 meters.
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Find the lengths of its sides.
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So we've got a picture here of a triangle.
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We've got three sides.
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And to get the perimeter of any shape, you simply add up the sides.
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So I'm going to add the three sides up, the first side.
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All right, plus the second side.
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It's the second side, right?
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Plus the third side is 85.
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Because it says the perimeter is 85.
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All right, so let's simplify the left hand side.
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I've got x squared plus 4x plus 8 equals 85.
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All right, this is a quadratic because it has an x squared term.
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So we're going to have to set this equal to 0 in factor.
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So x squared plus 4x.
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All right, if I subtract 85 from both sides, do that.
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You should have minus 77.
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Subtracting 85 from both sides.
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OK, again, next step would be the factor.
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So we have x and x.
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All right, so we need factors of 77.
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We have to have a difference of 4.
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Well, there's not that many factors of 77.
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7 and 11 sort of screams out at me.
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And I want to have a plus and front of the 11
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and a minus and front of the 7 to get the plus 4x.
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All right, so x minus 7 is 0 or x plus 11 is 0.
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So x could be 7 or x could be negative 11.
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All right, let's see if x could be 7.
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Well, if we put in a 7 here, that side would be 14, 2 times 7.
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So we know one possibility is this would be 14.
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All right, if we put in a 7 here, we'd have 2 times 7,
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which is 14 plus 5.
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That would be 19.
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And if we put a 7 here, we have 7 squared, which
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is 49 plus 3.
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That's 52.
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So the question is, could that be the lengths of the sides?
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Actually, no.
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Because if 2 sides only add up to 13, I mean, I'm sorry, 14
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and 19 add up to 33, the last side is going
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to have to be smaller than 33.
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So x equals 7 is not a solution.
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OK?
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All right, now let's look at x equals negative 11.
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So we tried that.
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Let's just draw the picture again.
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Conventional self, that if you add the two smaller sides
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together, it's got to be bigger than the third side.
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That's why this triangle can't exist.
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You can't have a triangle like that.
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Although it looks like, if you're not careful,
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you might think that's the answer.
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All right, let's put in negative 11 for x.
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Well, if it had 2 times negative 11, that'd be negative 22.
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OK, forget that right there.
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OK, you know what?
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There's no solution.
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To the sun.