Question

A rope that is 245cm long is cut into three pieces. The ratio of the lengths of the first piece to the second piece is 2/3, and the ratio of the lenghts of the second piece to the third piece is 4/5. What is the length of the longest of the the three pieces?

Answer 1

The length of the longest piece of the cut rope is; 105 cm

How to work with ratios?

We are given that;

Length of rope = 245 cm

We need to make the ratio of second piece equal in both the ratio to find the ratio of all three pieces.

2:3

4:5

Multiply 1st ratio by 4 and 2nd ratio by 3:

Now, the ratio becomes: 8:12 and 12:15

And the ratio of three pieces can be represented as:

8: 12: 15, this ratio is the first piece: second piece: third piece

Thus;

8x + 12x + 15x = 245

35x = 245

x = 245/35

So, the pieces lengths will be;

First piece = 8 * 7 = 56 cm

Second piece = 12 * 7 = 84 cm

Third piece = 15 * 7 = 105 cm

Read more about ratios at; https://brainly.com/question/2784798

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