1) suppose for purposes of calculation that the cake is inscribed in a square of 8 by 8
the area of 1 cake=8*8=64 in²
the rectangular table area=576 in²-----> I assume square table 24 in x 24 in
576/64= 9----------- > Sue has baked 9 cakes
if just 1 carrot cake
then
(9-1)=8 ----------> coffee cakes and lemon cakes
we know that equal numbers of coffee cakes and lemon cakes
therefore
coffee cakes=8/2=4
lemon cakes=4
carrot cake=1
the answer part 1) is
the dimensions of the table are 24 in x 24 in
the answer part 2) is
Sue has baked 9 cakes
coffee cakes=4
lemon cakes=4
carrot cake=1
part 3) distribution of the cakes in the table 24 in x 24 in
answer
let
Z------->carrot cake
C------->coffee cakes
L------->lemon cakes
Z-C-L or C-L-C
C-L-C Z-C-L
L-C-L C-L-C
4x - 3 = 9
4x = 9 + 3
4x = 12
x = 3
hope that helps, God bless!
3 and 8 are legs of a right triangle. we are looking for the hypotenuse. therefore a²+b²=c²
3²+8²=c²
9+64=c²
73=c²
c=✓73 or about 8.544