anonymous
  • anonymous
Equilateral Triangle MNP has perimeter 12a+18b. Line segment QR is a midsegment. What is QR?
Geometry
chestercat
  • chestercat
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jdoe0001
  • jdoe0001
got pic?
anonymous
  • anonymous
No...
DecentNabeel
  • DecentNabeel
With a perimeter = 12a + 18b, that means each side has length (12a + 18b) / 3 = 4a + 6b A midsegment creates a 30:60:90 triangle, with side lengths which are in the ratio of x:2x:sqrt(3)*x. In other words, the side opposite the 90 degree angle created by the midsegment, is one of the sides of the equilateral triangle, which we already know has length 4a + 6b. Therefore: ==> 4a + 6b = sqrt(3)*x ==> x = (4a+6b)/sqrt(3) However, we're looking for the length of the midsegment, which is the side opposite the 60 degree angle, which is = 2x. Therefore, QR = 2*x = 2*(4a+6b)/sqrt(3) ==> QR = (8a + 12b)/sqrt(3)

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