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$2$ . A garden's dimensions are $32$ feet by $18$ feet. How much fencing is needed if a fence will be constructed $7$ feet from the garden on all sides?

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Pythagorean Theorem and its converse

Full solution

Q.

2

. A garden's dimensions are

32

feet by

18

feet. How much fencing is needed if a fence will be constructed

7

feet from the garden on all sides?

Determine dimensions: Determine the dimensions of the area including the fence. The fence will be $7$ feet away from the garden on all sides, so we need to add $14$ feet to each dimension of the garden ( $7$ feet on each side). New length = $32$ feet + $14$ feet = $46$ feet New width = $18$ feet + $14$ feet = $32$ feet
Calculate perimeter: Calculate the perimeter of the area including the fence. $\newline$ Perimeter = $2 \times (\text{length} + \text{width})$ $\newline$ Perimeter = $2 \times (46 \, \text{feet} + 32 \, \text{feet})$ $\newline$ Perimeter = $2 \times 78 \, \text{feet}$ $\newline$ Perimeter = $156 \, \text{feet}$
Check calculation: Check the calculation for any mathematical errors. $\newline$ Re-checking the perimeter calculation: $\newline$ Perimeter = $2 \times (\text{length} + \text{width})$ $\newline$ Perimeter = $2 \times (46 \, \text{feet} + 32 \, \text{feet})$ $\newline$ Perimeter = $2 \times 78 \, \text{feet}$ $\newline$ Perimeter = $156 \, \text{feet}$ $\newline$ No mathematical errors are found in the calculation.

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