Trapeze problem?

It is given the trapeze with bases 1 cm and 7 cm. Find the length of the segment parallel with the bases that divides it in two parts with the same area.

Update:

I mean trapeze or trapezium. Not a triangle!

Comments

  • Let the length of the segment be L and let h1 and h be the partial height and the total height.

    (L+7)h1 = (1/2)(1+7)h, balanced by areas

    h1/(7-L) = h/(7-1), proportionality

    Simplify and combine the two equations,

    (L+7)/4 = h/h1 = 6/(7-L)

    Solve for L,

    7^2-L^2 = 24

    L = 5 cm

  • (1+x)/2 * h = (1+7)/2 * H/2

    (x+7)/2 * (H-h) = (1+7)/2 * H/2

    Use a little basic proportionality theorem in between. I'll leave that to u.

    While solving H gets eliminated and we get x = 5 cm

  • a trapeze is a triangle. go look up "formula for the area of a triangle".

  • 5cm

    A= (A+B)/2

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