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Calculate-the-side-of-an-equilateral-triangle-whose-vertices-are-situated-on-three-parallel-coplanar-lines-knowing-that-a-and-b-are-the-distances-of-the-parallel-line-to-the-others-




Question Number 76974 by Maclaurin Stickker last updated on 02/Jan/20
Calculate the side of an equilateral  triangle whose vertices are situated  on three parallel coplanar lines,  knowing that a and b are the distances  of the parallel line to the others.
Calculatethesideofanequilateraltrianglewhoseverticesaresituatedonthreeparallelcoplanarlines,knowingthataandbarethedistancesoftheparallellinetotheothers.
Answered by mr W last updated on 02/Jan/20
(√(l^2 −(a+b)^2 ))=(√(l^2 −b^2 ))−(√(l^2 −a^2 ))  l^2 −a^2 −b^2 −2ab=l^2 −b^2 +l^2 −a^2 −2(√((l^2 −b^2 )(l^2 −a^2 )))  l^2 +2ab=2(√((l^2 −b^2 )(l^2 −a^2 )))  l^4 +4abl^2 +4a^2 b^2 =4(l^2 −b^2 )(l^2 −a^2 )  3l^2 −4(a^2 +b^2 +ab)=0  ⇒l=2(√((a^2 +b^2 +ab)/3))
l2(a+b)2=l2b2l2a2l2a2b22ab=l2b2+l2a22(l2b2)(l2a2)l2+2ab=2(l2b2)(l2a2)l4+4abl2+4a2b2=4(l2b2)(l2a2)3l24(a2+b2+ab)=0l=2a2+b2+ab3
Commented by Maclaurin Stickker last updated on 02/Jan/20
how did you get the first expression?
howdidyougetthefirstexpression?
Commented by mr W last updated on 02/Jan/20
Commented by mr W last updated on 02/Jan/20
AB=(√(l^2 −b^2 ))  CD=(√(l^2 −(a+b)^2 ))  DE=(√(l^2 −a^2 ))  CD+DE=AB  (√(l^2 −(a+b)^2 ))+(√(l^2 −a^2 ))=(√(l^2 −b^2 ))
AB=l2b2CD=l2(a+b)2DE=l2a2CD+DE=ABl2(a+b)2+l2a2=l2b2

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