MathDB

A wooden beam

EFGH

ABCD

is with three cuts in

8

smaller ones sawn beams. Each cut is parallel to one of the three pair of opposit sides. Each pair of saw cuts is shown perpendicular to each other. The smaller bars at the corners

A, C, F

and

H

have a capacity of

9, 12, 8, 24

respectively.(The proportions in the picture are not correct!!). Calculate content of the entire bar.
[asy] unitsize (0.5 cm);
pair A, B, C, D, E, F, G, H; pair x, y, z;
x = (1,0.5); y = (-0.8,0.8); z = (0,1);
B = (0,0); C = 5*x; A = 3*y; F = 4*z; E = A + F; G = C + F; H = A + C + F;
fill(y--3*y--(3*y + z)--(y + z)--cycle, gray(0.8)); fill(2*x--5*x--(5*x + z)--(2*x + z)--cycle, gray(0.8)); fill((y + z)--(y + 4*z)--(y + 4*z + 2*x)--(4*z + 2*x)--(2*x + z)--z--cycle, gray(0.8)); fill((2*x + y + 4*z)--(2*x + 3*y + 4*z)--(5*x + 3*y + 4*z)--(5*x + y + 4*z)--cycle, gray(0.8)); draw(B--C--G--H--E--A--cycle); draw(B--F); draw(E--F); draw(G--F); draw(y--(y + 4*z)--(y + 4*z + 5*x)); draw(2*x--(2*x + 4*z)--(2*x + 4*z + 3*y)); draw((3*y + z)--z--(5*x + z));
label("

A

", A, SW); label("

B

", B, S); label("

C

", C, SE); label("

E

", E, NW); label("

F

", F, SE); label("

G

", G, NE); label("

H

", H, N); [/asy]

Problem Statement