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Four pieces of timber with the lengths in centimeters cm are positioned in parallel to each as shown.
A single cut is made along the line L perpendicular to the lengths of timbers so that the total length of timbers on each side of L is the same. What is the length of the top piece of timber to the left of L? (Figure not drawn to scale) 

To solve this problem, we need to balance the total lengths of the timber on both sides of the cutting line \( L \), as stated in the problem. The total length of the timber pieces to the left and to the right of \( L \) must be the same after the cut.

### Total Lengths Before the Cut:

- **Top piece of timber**: 500 cm
- **Second piece of timber**: 300 cm
- **Third piece of timber**: 200 cm
- **Fourth piece of timber**: 150 cm

### Distances of the pieces to the right of \( L \) (i.e., their lengths to the right of \( L \)):

- Top piece to the right of \( L \): 300 cm
- Second piece to the right of \( L \): 300 cm
- Third piece to the right of \( L \): 500 cm
- Fourth piece to the right of \( L \): 400 cm

### Step 1: Find the total lengths to the right of \( L \)
Add the lengths of all the portions to the right of \( L \):

\[
300 + 300 + 500 + 400 = 1500 \, \text{cm}
\]

### Step 2: Total Length of All Timbers
Now, the total length of all timbers combined (i.e., all four pieces before the cut):

\[
500 + 300 + 200 + 150 = 1150 \, \text{cm}
\]

To make the cut balanced, the length to the left of \( L \) must be:

\[
\frac{1500}{2} = 750 \, \text{cm}
\]



Four pieces of timber with the lengths in centimeters cm are positioned in parallel to each as shown. A single cut is made along the line L perpendicular to the lengths of timbers so that the total length of timbers on each side of L is the same. What is the length of the top piece of timber to the left of L?

Find out how to balance the total lengths of four timber pieces by making a single perpendicular cut. This problem explores key geometry and algebra concepts, requiring the calculation of total lengths on either side of the cut. Suitable for Grades 6-8.

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