The diagram shows an L-shaped school garden (not drawn to scale). The total perimeter of the garden is 52 m. Four of the six side lengths are labelled: the top segment is 8 m, the step-down is 4 m, the inner horizontal is 8 m, and the full bottom is 16 m. The left side and right side are not labelled. The left side is 4 m longer than the right side. What is the total area of the L-shaped garden?
Show Worked Solution
Worked Solution
Step 1: Find the sum of the two unlabelled sides using the perimeter.
Perimeter = 8 + 4 + 8 + right side + 16 + left side = 52
36 + right side + left side = 52
right side + left side = 16 m
Step 2: Use the given relationship to find each side.
Left side = right side + 4
Substitute: (right side + 4) + right side = 16
2 x right side = 12
Right side = 6 m
Left side = 6 + 4 = 10 m
Step 3: Split the L-shape into two non-overlapping rectangles.
Left rectangle: 8 m wide x 10 m tall = 80 m²
Right rectangle: 8 m wide x 6 m tall = 48 m²
Step 4: Total area = 80 + 48 = 128 m²
Correct answer: 128 m²
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