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!
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