A piece of wood is divided in 3 pieces in the ratio 3:4:2. The length of the longest piece is 72. Calculate the length of the piece of wood.
72/4 = 18
72 + 18*3 + 18*2 = ?
To find the length of the entire piece of wood, we need to determine the total ratio of the three pieces.
The ratio of the lengths of the three pieces is given as 3:4:2.
Step 1: Find the total ratio:
Adding the three numbers in the ratio, we get 3 + 4 + 2 = 9.
Step 2: Calculate the length of the whole piece of wood:
Since the longest piece has a length of 72, we can set up the following equation:
(Length of longest piece) / (Total ratio) = (Length of whole piece)
72 / 9 = 8.
Therefore, the length of the entire piece of wood is 8.
To solve this problem, we can first set up a proportion using the given ratio. Let's denote the length of the piece of wood as 'x'.
According to the given ratio, the lengths of the three pieces are in the ratio 3:4:2. So we can write the proportion:
(Length of longest piece) / (Length of second longest piece) = (Ratio of longest piece) / (Ratio of second longest piece)
Plugging in the values from the problem, we have:
72 / (4x) = 3 / 4
To solve for 'x', we can cross-multiply and then solve for 'x':
72 * 4 = 3 * (4x)
288 = 12x
x = 288 / 12
x = 24
Therefore, the length of the entire piece of wood is 24 units.