A board, 39 cm long is cut into three pieces such that the second piece is twice as long as the first and the third is 4 cm longer than the second.
If the 1st piece is x, then
x + 2x + 2x+4 = 39
Now just find x and the rest follows.
Let's represent the length of the first piece as x cm.
According to the given information:
- The second piece is twice as long as the first, so its length is 2x cm.
- The third piece is 4 cm longer than the second, so its length is 2x + 4 cm.
We also know that the total length of the board is 39 cm, so we can set up the following equation:
x + 2x + (2x + 4) = 39
Now, let's solve the equation to find the value of x:
5x + 4 = 39
5x = 35
x = 7
Therefore, the length of the first piece is 7 cm.
To find the lengths of the second and third pieces, we can substitute the value of x:
The second piece: 2x = 2 * 7 = 14 cm
The third piece: 2x + 4 = 2 * 7 + 4 = 18 cm
So, the lengths of the pieces are:
- The first piece: 7 cm
- The second piece: 14 cm
- The third piece: 18 cm
To solve this problem, let's assign variables to represent the lengths of the three pieces of the board.
Let the length of the first piece be x cm.
According to the problem, the second piece is twice as long as the first piece, so its length would be 2x cm.
Similarly, the third piece is 4 cm longer than the second piece, so its length would be (2x + 4) cm.
Now, we can form an equation based on the given information: the sum of the lengths of the three pieces is equal to the total length of the board.
x + 2x + (2x + 4) = 39
Simplifying the equation:
5x + 4 = 39
Subtracting 4 from both sides:
5x = 35
Dividing by 5:
x = 7
Now, the length of the first piece (x) is 7 cm.
The length of the second piece is twice the first piece, so it is 2 * 7 = 14 cm.
Finally, the length of the third piece is 4 cm longer than the second piece, making it 14 + 4 = 18 cm.
Therefore, the lengths of the three pieces are 7 cm, 14 cm, and 18 cm, respectively.