Three pieces of wood are needed for a project.
They are to be cut from a 90-cm-long piece of
wood. The longest piece is to be 3 times as long as
the middle-sized piece and the shortest piece is to
be 10 cm shorter than the middle-sized piece. Can
this be done with two cuts? If so, tell how.
The pieces are 10 cm, 20 cm, and 60 cm. I don't think this can be done with two cuts. I think that you woudl need three.
After cutting off a 60 cm piece, and 20 cm off the remaining 40 cm, you will be left with 10 cm. That is two cuts. You could also change the order.
To determine if it is possible to cut three pieces of wood as described using two cuts, let's break it down step-by-step:
1. Let's calculate the length of the middle-sized piece of wood. We know that the longest piece is 3 times as long as the middle-sized piece, and the shortest piece is 10 cm shorter than the middle-sized piece.
Let's represent the middle-sized piece of wood as x cm. Therefore, the longest piece will be 3x cm, and the shortest piece will be (x - 10) cm.
2. The total length of the three pieces of wood must equal the length of the original 90-cm-long piece of wood.
Therefore, we need to set up an equation: x + 3x + (x - 10) = 90
Simplifying the equation: 5x - 10 = 90
3. Now, let's solve the equation to find the value of x:
5x - 10 = 90
5x = 100
x = 20
So, the middle-sized piece of wood should be 20 cm long.
4. Now, we know the length of the middle-sized piece, which is 20 cm. Using this information, we can find the lengths of the longest and shortest pieces:
- The longest piece: 3 * 20 = 60 cm
- The shortest piece: 20 - 10 = 10 cm
5. Finally, let's check if it is possible to obtain these three pieces using two cuts. For this, we need to determine if the sum of the two cuts is greater than or equal to the longest piece's length (60 cm).
Since the total length of the original piece of wood is 90 cm and the shortest piece is 10 cm, the sum of the two cuts should be at least 80 cm to obtain a 60 cm longest piece.
Therefore, cutting two equal lengths of 40 cm each from the original 90-cm-long piece of wood should work. This will leave shortened pieces totaling 50 cm, from which you can then cut a 20 cm middle-sized piece and a 10 cm shortest piece.
Therefore, yes, it is possible to obtain the three required pieces by making two cuts.