Question

A board, 77 cm long is cut into three pieces such that the second piece is twice as long as the first and the third 7 cm longer than the second. Find the length of the shorter piece. Cm

Answer 1

Given:

The length of the board is 77 cm.

Let a be the length of the first piece.

Let b be the length of the second piece.

Let c be the length of the third piece.

Given that the second piece is twice as long as the first.

`b=2a`

Given that the third is 7 cm longer than the second.

`c=b+7`

Substitute b=2a, we get

`c=2a+7`

The sum of the three pieces =The length of the board.

`a+b+c=77`

Substitute b=2a and c=2a+7, we get

`a+2a+2a+7=77`

`5a+7=77`

Subtracting 7 from both sides, we get

`5a+7-7=77-7`

`5a=70`

Dividing both sides by 5, we get

`(5a)/(5)=(70)/(5)`
`a=14cm`

Substitute a=14cm in b=2a and c=2a+7, we get

`b=2*14=28cm`
`c=2*14+7=35cm`

Hence the length of the shorter piece is 14cm.