Question

There are 5 posts supporting the guard rail for the steps to your home the tallest post is 3 feet tall the height of each of the other post is 5/6 the height of the next larger post.

write an expression what is the height of the shortest post?

Answer 1

Given,

The number posts = 5,

Which are placing in ascending order,

Also, every post is
`(5)/(6)` of the height of the next larger post.

If the larger post has the height of 3 feet,

Then the height of second larger post =
`3* (5)/(6)`

Height of third larger post =
`3* (5)/(6)* (5)/(6)`

Height of fourth larger post =
`3* (5)/(6)* (5)/(6)* (5)/(6)`

Height of fifth larger post or smallest post =
`3* (5)/(6)* (5)/(6)* (5)/(6)* (5)/(6)`

Which is the required expression,

By solving it,

The height of the smallest post =
`3* (625)/(1296)` = 1.45 feet ( approx )