0

# 3 to 4 ratio

THERE ARE 3 SIMILAR INCH MEASUREMENTS.

THE RATIO OF MEASUREMENT A TO MEASUREMENT B IS 5 TO 8 INCHES.

THE RATIO OF THE MEASUREMENT B TO C IS 3 TO 4.

WHAT IS THE RATIO OF TRIANGLE A TO C? ---- AND WHAT ARE THE CALCULATIONS?

I cannot understand why both comparisons are included for calculation purposes.

B to C is a 3 to 4 comparison - which means that C is 1/4 bigger than B or 10 (8 x 125% = 10).  Why would the calculation of this comparison be included in the calculation of the first comparison?

Yes, after you arrive at the result of the 3 to 4 relationship (10), then you'd use that answer to compare to 5.  So A to C would be 1 to 2.
When you said ratio of triangle A to C I assumed area of a triangle, thus I assumed 5 to 8 and 3 to 4 to be area ratios. If I assumed wrong, then you can repost the problem and give more information.
Arthur D.
After more consideration, look at these examples.
Triangle A has height 15 and base 30.
Triangle B has height 24 and base 48.
Triangle C has height 32 and base 64.
The ratio of height A to height B is 15/24=5/8 and 30/48=5/8 also.
The ratio of height B to height C is 24/32=3/4 and 48/64=3/4 also.
The ratio of height A to height C is 15/32 and 30/64=15/32 also.
The ratio of the area of triangle A to triangle C is (0.5*15*30)/(0.5*32*64)=225/1024

### 1 Answer by Expert Tutors

Arthur D. | Effective Mathematics TutorEffective Mathematics Tutor
5.0 5.0 (7 lesson ratings) (7)
0
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.