A concrete border is to be built around a triangular flower garden that has sides of 10 m, 7 m and 8 m. The border is to be 1 m wide on all sides of the garden. Before the concrete can be poured, wooden forms needs to be placed on the inside and outside perimeter of the border. Determine the total length of wood needed to build the forms.
Two good solutions are provided by Reiny and MathMate in the related questions below.
To determine the total length of wood needed to build the forms, we need to calculate the perimeter of the inner and outer borders separately and then add them together.
1. Calculate the perimeter of the inner border:
The inner border is formed by reducing the length of each side of the triangular garden by 1 meter.
The new lengths of the sides become 10 m - 2 m (reducing 1 m from each side), 7 m - 2 m and 8 m - 2 m.
The perimeter of the inner border is the sum of these reduced lengths of the sides.
Perimeter_inner = (10 m - 2 m) + (7 m - 2 m) + (8 m - 2 m)
2. Calculate the perimeter of the outer border:
The outer border is formed by increasing the length of each side of the triangular garden by 1 meter.
The new lengths of the sides become 10 m + 2 m (increasing 1 m to each side), 7 m + 2 m, and 8 m + 2 m.
The perimeter of the outer border is the sum of these increased lengths of the sides.
Perimeter_outer = (10 m + 2 m) + (7 m + 2 m) + (8 m + 2 m)
3. Calculate the total length of wood needed by summing the perimeters of the inner and outer borders:
Total_length_wood = Perimeter_inner + Perimeter_outer
Now you can substitute the values in the above formulas to find the answer.