If the rectangular faces of a brick have their diagonals in the ratio 3 : 2 \sqrt{3} : \sqrt{15}, what is the ratio of the length of the shortest edge of the brick to that of its longest edge?
+357 Let a, b, and c be length of the three sides of the brick.
From the ratios given, we can write these equations.
(1) (a^2+b^2)=(3)^2=9
(2) (b^2+c^2)=(2√3)^2=12
(3) (a^2+c^2)=(√15)^2=15
(1)+(2)+(3)
2*(a^2+b^2+c^2)=36
(a^2+b^2+c^2)=18
(9+c^2)=18
c^2=9
(2)
(b^2+c^2)=12
(b^2+9)=12
b^2=3
(1)
(a^2+b^2)=9
(a^2+3)=9
a^2=6
(I put too much effort into this... why didn't I just use sqrt(#) whatever)
The longest and shortest are c, b.
b^2:c^2=3:9=1:3
So B:C=1:√3
Yay!
