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.
Answer 162
72/4 = 18
So, multiply all the lengths by 18 to get
54+72+36 = 162
Why did the piece of wood become a mathematician? Because it was great at dividing and solving ratios! So let's put on our mathematician hats and solve this problem together.
We are given that the longest piece is in a ratio of 3:4:2. Since the longest piece has a length of 72, we can set up the equation 3x = 72, where x represents the scale factor.
Dividing 72 by 3, we find that x = 24. Now we can find the length of the entire piece of wood by adding up the lengths of the three pieces: 3x + 4x + 2x = 9x.
Plugging in the value of x, we get 9 * 24 = 216.
So the length of the piece of wood is 216.
But hey, the fun doesn't stop there! If you're feeling extra silly, you can tell people that a wood magician made the piece of wood longer with a magic spell! Abracadabra, the piece of wood became 216 units long!
To solve this problem, you can use the concept of ratios.
Let the total length of the piece of wood be x.
According to the given ratio, the lengths of the three pieces are:
3x/9, 4x/9, and 2x/9.
Given that the length of the longest piece is 72, we can set up the following equation:
4x/9 = 72
To solve for x, we can cross-multiply and then solve for x:
4x = 72 * 9
4x = 648
x = 648/4
x = 162
Therefore, the length of the piece of wood is 162.
To find the length of the entire piece of wood, we need to first determine the total ratio of the three pieces.
In this case, the ratio of the three pieces is 3:4:2.
To calculate the length of the longest piece, we divide 72 by the ratio of the longest piece, which is 4.
So, 72 divided by 4 equals 18.
Now we know that the longest piece is 18 units long.
To find the total length of the wood, we add up the lengths of the three pieces.
The total ratio of the three pieces is 3+4+2, which equals 9.
We can set up a proportion to find the length of the entire piece of wood:
18 (length of longest piece) is to 9 (total ratio) as X (length of entire piece) is to 1.
By cross-multiplying, we find that X is equal to 18 multiplied by 1, which equals 18.
Therefore, the length of the entire piece of wood is 18 units.