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.
make the first cut at 6cm and the second at 22cm. You will have 3 pieces that measure 6cm, 16cm and 48cm.
you mark off 10cm and 30cm on the original piece of wood and you cut at your marks this will give you 3 pieces a 10cm piece, 20cm piece, and a 60cm piece of wood and it works out because the pieces add up to 90cm
fyi the answer above doesnt add up to the required 90cm
i gave the second answer
To determine if it is possible to cut the three pieces of wood with two cuts, we need to analyze the given information and see if we can find a solution.
Let's represent the lengths of the three pieces of wood as follows:
- Longest piece: L
- Middle-sized piece: M
- Shortest piece: S
From the given information, we have three conditions:
1. The longest piece is to be 3 times as long as the middle-sized piece: L = 3M
2. The shortest piece is to be 10 cm shorter than the middle-sized piece: S = M - 10
3. The sum of all three pieces should be equal to the length of the original 90-cm-long piece of wood: L + M + S = 90
Now let's substitute the values of L and S from the first two conditions into the third condition:
3M + M + (M - 10) = 90
Simplifying the equation:
5M - 10 = 90
Adding 10 to both sides:
5M = 100
Dividing both sides by 5:
M = 20
Now that we've found the length of the middle-sized piece (M = 20), we can determine the lengths of the longest and shortest pieces using the first two conditions:
L = 3M = 3 * 20 = 60
S = M - 10 = 20 - 10 = 10
So, the three pieces of wood would be 60 cm, 20 cm, and 10 cm in length.
To cut these pieces with only two cuts, we can follow these steps:
1. Make the first cut at 20 cm from one end of the 90-cm-long piece of wood. This will give us a piece that is exactly 20 cm long.
2. Make the second cut at 60 cm from the same end. This will give us two pieces: one 60 cm long and one 10 cm long.
Therefore, it is possible to cut the three pieces of wood (60 cm, 20 cm, and 10 cm) with two cuts.