The sum of the numerator and the denominator of the certain fraction is equal to 4,140. When the fraction was reduced, the result was 713 . What was the original fraction?

1449/2691

Step-by-step explanation:

We must start from the fraction that is 7/13. Now, we know that it was simplified, with trial and error we can reach the result.

First, let's multiply both by 200:

7 * 200 = 1400

13 * 200 = 2600

1400 + 2600 = 4000

It means that we are missing 140, to reach the objective, that is, we are close, let's try 205 now:

7 * 205 = 1435

13 * 205 = 2665

1435 + 2665 = 4100

We get even closer, only 40 missing, let's try 207 below:

7 * 205 = 1449

13 * 205 = 2691

1449 + 2691 = 4140

We managed to get to the corresponding numbers, therefore the original fraction was 1449/2691

d. bc = 12 and ef = 16

step-by-step explanation:

we are given that δabc : δdef such that .

also, it is given that

so, from the options, we need that .

a.

b.

c.  

d.

as, we can see that only option d gives the same ratio as i.e. .

hence, the possible lengths are bc = 12 and ef = 16.