Piasofiaidn
Answered

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A rope is cut into 3 parts in the ratio 3:4:6. The length of the shortest part is 54 cm. What is the length of the longest part?

Sagot :

AwesomeHelperidn
3 : 4 : 6
What is the shortest one?
Yeah, it is 3. Replace it with 54.

54 : 4 : 6
You increased with 54, now how many "3's" did you increased? 
That is 54/3 = 18.

To find the corresponding value of 4 and 6 on the ratio, multiply it by 18.
4 * 18 = 72
6 * 18 = 108

Check:
54 : 72 : 108                        << ------  the answer is 108
54/3 : 72/4 : 108/6
18 : 18 : 18

The first and the shortest part is 54cm, as said.
The second and the average part is 72cm.
The third and the longest part is 108cm.
And the rope is totally 234cm
Let x be the constant:

3x + 4x + 6x = 54 cm + 4x + 6x

13x = 54 cm + 10 x

13x - 10x = 54 cm

3x = 54
 3     3

x = 18 cm

The shortest is 3x = 54 cm (given)
3 (18 cm) = 54 cm
  54 cm = 54 cm

The longest is 6x;
Length of Longest part = 6 (18 cm)
Length of longest part =  108 cm.

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