Use the image to answer the question.
A composite of two rectangles. The top rectangle is a smaller rectangle and is centered on the top width of the bottom larger rectangle. The top rectangle has a label of 4 meters on the top side, and 3 meters on the left side. The top two angles of the top rectangle have right angle marks. The bottom rectangle has a label of 8 meters on the bottom side. The distance between the right side of the top rectangle to the right side of the bottom rectangle is 2 meters. All 4 angles of the bottom rectangle have right angle marks.
The area of the composite figure is 52 square meters. What is the value in meters of the height of the larger rectangle?(1 point)
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To find the height of the larger rectangle, we need to first find the width of the larger rectangle. The width of the larger rectangle is the sum of the width of the top rectangle and the distance between the right side of the top rectangle to the right side of the bottom rectangle, which is 4 meters + 2 meters = 6 meters.
Let the height of the larger rectangle be h meters. The area of the larger rectangle is then given by:
Area = width x height
52 = 6 x h
52 = 6h
h = 52 / 6
h = 8.67 meters
Therefore, the value of the height of the larger rectangle is 8.67 meters.