A piece of wooden rod 31 cm long is to be cut into three parts, two of which are to be of equal length. the length of each of the two equal part is 5 cm longer than third part. find their lengths.
solution pls.
third part --- x
other part --- x+5 each
solve:
x + x+5 + x+5 = 31
To find the lengths of the three parts, let's assign variables to represent the lengths.
Let's assume the length of the third part is x cm.
According to the problem, the two equal parts are 5 cm longer than the third part. So, the length of each of the two equal parts is x + 5 cm.
Now, since we need to divide the wooden rod into three parts, the sum of the lengths of the three parts must be equal to the length of the rod, which is 31 cm.
Therefore, the equation representing this situation is:
x + (x + 5) + (x + 5) = 31
Now, let's solve this equation to find the value of x.
Combining the like terms:
3x + 10 = 31
Subtracting 10 from both sides:
3x = 21
Dividing both sides by 3:
x = 7
Now that we have found the value of x, we can find the lengths of the three parts:
- The length of the third part = x = 7 cm
- The length of the two equal parts = x + 5 = 7 + 5 = 12 cm
Therefore, the lengths of the three parts are:
- The first part: 7 cm
- The second part: 12 cm
- The third part: 12 cm