Question

A rope that is 245 cm 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 lengths of the second piece to the third piece is 4:5. What is the length of the longest of the three pieces?

Answer 1

The length of longest piece is 105 cm.

Explanation:

Given:

Rope is 245 cm long.

Ratio of lengths of first to second piece = 2:3.

Ratio of lengths of second to third piece = 4:5.

To find:

Length of longest piece = ?

Solution:

We are given the ratio of first and second pieces AND

ratio of second and third pieces.

Common link is second piece.

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

`\Rightarrow 8x+12x+15x = 245\\\Rightarrow 35x = 245\\\Rightarrow x = (245)/(35)\\\Rightarrow x = 7`

So, the pieces lengths will be

First piece =
`8 * 7 = 56` cm

Second piece =
`12 * 7 = 84` cm

Third piece =
`15 * 7 = 105` cm

So, the length of longest piece is 105 cm.