A pool fence is to be placed around a rectangular pool that is 6 m by 8 m.Question 1Workboarda. If the fence is to be 1 m away from the edge of the pool and also rectangular in shape, what length of fencing is required? (Include the width of the gate in the length of the fence.)Perimeter = mSUBMIT (ATTEMPT 1 OF 2)Question 2Workboardb. If 𝑙 represents the length of any pool and 𝑤 represents the width of any pool, write a rule that relates the total length of pool fencing to 𝑙 and 𝑤.Fence length =
Question
A pool fence is to be placed around a rectangular pool that is 6 m by 8 m.Question 1Workboarda. If the fence is to be 1 m away from the edge of the pool and also rectangular in shape, what length of fencing is required? (Include the width of the gate in the length of the fence.)Perimeter = mSUBMIT (ATTEMPT 1 OF 2)Question 2Workboardb. If 𝑙 represents the length of any pool and 𝑤 represents the width of any pool, write a rule that relates the total length of pool fencing to 𝑙 and 𝑤.Fence length =
Solution
Question 1: First, we need to calculate the dimensions of the area that the fence will enclose. Since the fence is to be 1 m away from the edge of the pool on all sides, we add 2 m to both the length and the width of the pool. This gives us a length of 8 m + 2 m = 10 m and a width of 6 m + 2 m = 8 m for the fenced area.
The length of fencing required is the perimeter of this area. The formula for the perimeter of a rectangle is 2*(length + width).
So, the length of fencing required is 2*(10 m + 8 m) = 36 m.
Question 2: If l represents the length of any pool and w represents the width of any pool, and the fence is to be 1 m away from the edge of the pool on all sides, then the length of the fence is given by the formula 2*((l + 2) + (w + 2)).
So, the rule that relates the total length of pool fencing to l and w is: Fence length = 2*(l + w + 4).
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