A vertical line divides the triangle whose vertices are at (0,0), (1,1), and (9,1) into two parts; a triangle and a quadrilateral. If the areas of the triangle and the quadrilateral are equal, what is the equation of the vertical line?
A vertical line divides the triangle whose vertices are at (0,0), (1,1), and (9,1) into two parts; a triangle and a quadrilateral. If the areas of the triangle and the quadrilateral are equal, what is the equation of the vertical line?
from the diagram,
considering the area of the small triangle,find the area of it
If A is the area of the larger triangle,
substitute A, A1, (A+A') and A' with d and a
this is when vertical line meets AB
do the same thing when the vertical line meets CA
Ok, now that you've been shown how, try this similar one:
A vertical line divides the triangle whose vertices are at (0,0), (7,24), and (32,24) into two parts;
a triangle and a quadrilateral. If the areas of the triangle and the quadrilateral are equal,
what is the LENGTH of the vertical line?
You'll find that all side lengths (plus the areas) are integers;
smallest case, I believe, for an all-integer.
SOLUTION (since no response!):
A(0,0), B(7,24), C(32,24)
u=7,v=32,w=24 : so A(0,0), B(u,w), C(v,w)
Vertical line length = wSQRT[(v - u) / (2v)] = 15
Smallest all-integer case is smaller than I thought: A(0,0), B(4,15), C(36,15) ; vertical line = 10