Question

a line is divided into three parts. the first part is two-thirds the length of the second part, the third part is 1÷2 cmshorter than the first part and 2 cm shorter than the second part. what is the length of the lines?

Answer 1

The length of the lines are 3 cm, 4.5 cm and 2.5 cm respectively.

Step-by-step explanation:

Let the three line segments, partly divided from a line are of length x cm, y cm and z cm respectively.

By the given conditions,

x = 2/3 * y .....(1)

z = x - 1/2 .....(2)

z = y - 2 .....(3)

From (2), y = 3x/2

From (3), z = x - 1/2

Substituting the above two values in (3), we get

x - 1/2 = 3x/2 - 2

or, 3x/2 - x = 2 - 1/2

or, (3/2 - 1) x = (4 - 1)/2

or, 1/2 * x = 3/2

or, x = 3

Then y = 3/2 * 3 = 9/2 = 4.5

and z = 3 - 1/2 = (6 - 1)/2 = 5/2 = 2.5

Therefore the length of the three line segments are 3 cm, 4.5 cm and 2.5 cm respectively.