# 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?

2
by piasofia

2015-10-12T18:59:37+08:00

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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

• Brainly User
2015-10-12T23:39:14+08:00

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Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
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.