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The scale diagram represents the plan of a garden. The garden is bounded by a house, a hedge, a wall, and a fence. A bush is to be planted in the garden. The bush must be at least 4m in front of the tree marked T. It must also be closer to the wall than the fence. Using the scale 1cm to represent 2m, shade the region in which the bush can be planted.

User Hermeslm
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1 Answer

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Firstly, we have to understand the constraints of the problem and translate them into our diagram:

1. "The bush must be at least 4m in front of the tree marked T". This translates into a circle around the tree with a radius of 4m, where everything inside that circle is not a valid area for planting the bush. If we convert this into our scale of 1cm = 2m, then this would be a circle of radius 2cm around the tree.

2. "It must be closer to the wall than the fence". If we were to draw a line equidistant between the fence and the wall, the area closer to the wall would be the valid region for planting the bush.

Now, let's represent these conditions on our diagram:

1. Draw a circle around the tree with a radius of 2cm. Make sure to center your compass on the spot marked as the tree before drawing. This demarcates the area where the bush should not be planted.

2. Next, identify the positions of the fence and the wall in your diagram. Draw a line exactly in the middle of them, this line will differentiate between the side closer to the wall and the side closer to the fence.

3. Now, we have two regions identified on the diagram - one from the circle around the tree and one from the fence-wall midpoint. Your area of interest, where the bush can be planted, is the area that falls within the wall side (close to the wall than fence) and outside the circle around the tree.

4. To finalize your solution, visually identify this common area within these two regions and shade it appropriately.

Keep in mind, the exact details of these steps might differ based on how the elements are arranged in your garden plan. Also, while doing your shading, take care not to shade over the regions representing the house or the other barriers. Your solution should make it clear where the bush can be safely planted without interference.

User UYSIZfoz
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