Answer:
39.2
Explanation:
We need a ratio of 3:7.
Let's multiply both numbers by 2.
6:14
Add them: 6 + 14 = 20
6:14 is the same ratio as 3:7, but 6 and 14 cannot be the answer since their sum is only 20.
Let's try 3. We now have the numbers 9 and 21.
Again, 9 + 21 = 30 which is much less than 56.
We need to find a multiplier that we multiply both 3 and 7 by. We multiply both 3 and 7 by that multiplier to get two new numbers in the ratio of 3:7. Then when we add the new numbers, we get 56.
Let the multiplier be x.
3x + 7x = 56
10x = 56
x = 5.6
The multiplier is 5.6
Now we multiply both 3 and 7 by the multiplier 5.6
3 × 5.6 = 16.8
7 × 5.6 = 39.2
The numbers 16.8 and 39.2 are in the ratio 3:7.
Also, since 16.8 + 39.2 = 56, they add to 56.
The longer length is 39.2