A to B is 5 to 8, B to C is 3 to 4
B=8 and B=3 in the two ratios
make the two B's the same number
8*3=24 and 3*8=24
5/8=?/24 and 3/4= 24/?
?=15 in the first equation and ?=32 in the second equation
5/8 becomes 15/24 and 3/4 becomes 24/32
now we have A to B is 15 to 24, B to C is 24 to 32
A=15, B=24, and C=32
therefore A to C is 15 to 32 or 15/32
Note:If the ratios are segment ratios(base and height), then 15/32 is a ratio of height to height or base to base. Let triangle A have base 30 and height 15, let triangle B have base 48 and height 24, and let triangle C have base 64 and height 32. The ratios of base to base and height to height are 5/8 and 3/4 as stated.
The area of triangle A to triangle C is (0.5*15*30)/(0.5*32*64)=225/1024.
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