a piece of wood is divided into three pieces in the ratio 3 : 4: 2. the length of the longest piece is 72 cm. calculate the length of the pices of wood
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To find the lengths of the three pieces of wood, we first need to determine the total ratio. The given ratio is 3:4:2, which represents the lengths of the three pieces.
To find the total ratio, we add the three parts: 3 + 4 + 2 = 9.
Next, we divide the length of the longest piece, which is 72 cm, by the total ratio:
72 cm / 9 = 8 cm.
This means that each part of the ratio represents 8 cm. Now, we can find the lengths of the three pieces by multiplying the parts by 8 cm:
First piece: 3 parts x 8 cm = 24 cm
Second piece: 4 parts x 8 cm = 32 cm
Third piece: 2 parts x 8 cm = 16 cm
So, the lengths of the three pieces of wood are 24 cm, 32 cm, and 16 cm.
To determine the lengths of the pieces of wood, we can start by understanding the given ratio: 3 : 4 : 2. This implies that the total ratio is divided into 3 parts, with the first part being 3, the second part being 4, and the third part being 2.
Let's assume the common ratio factor is 'x,' which will help us calculate the actual lengths. Therefore, the length of the first piece can be calculated by multiplying the first part of the ratio (3) by 'x', the length of the second piece is the second part (4) multiplied by 'x', and the length of the third piece is the third part (2) multiplied by 'x'.
So, we have:
Length of the first piece = 3x
Length of the second piece = 4x
Length of the third piece = 2x
We are given that the length of the longest piece is 72 cm, which corresponds to the second piece (4x). Therefore, we can now set up an equation:
4x = 72
To find the value of 'x,' we divide both sides of the equation by 4:
4x/4 = 72/4
x = 18
Now that we have the value of 'x,' we can substitute it into the expressions for each piece's length:
Length of the first piece = 3x = 3 * 18 = 54 cm
Length of the second piece = 4x = 4 * 18 = 72 cm
Length of the third piece = 2x = 2 * 18 = 36 cm
Therefore, the lengths of the three pieces of wood are 54 cm, 72 cm, and 36 cm.
let their lengths be 3x, 4x, and 2x
3x+4x+2x = 72
solve for x, then sub back into my definitions