A 12-foot board is divided into two pieces so one piece is twice as long as the other. What are the lengths?

Question

7097 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-08-28T10:02:13

Shorter piece: $4$ $4$ $ft.$ $"ft."$

Longer piece: $8$ $8$ $ft.$ $"ft."$

The two pieces are such that one piece is twice as long as the other.

So if the length of the shorter piece is $x$ $x$ , the length of the other must be $2 x$ $2 x$ .

Then, the total length is $x + 2 x = 12$ $x + 2 x = 12$ $ft. \Rightarrow 3 x = 12$ $"ft." Rightarrow 3 x = 12$ $ft.$ $"ft."$ .

If we solve the equation $3 x = 12$ $3 x = 12$ $ft.$ $"ft."$ for $x$ $x$ , we will find the length of the shorter piece:

$\Rightarrow 3 x = 12$ $Rightarrow 3 x = 12$ $ft.$ $"ft."$

$therefore x = 4$ $"ft."$

So the length of the longer piece is $2 x = 2 times 4$ $"ft."$ $= 8$ $"ft."$ .