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 break down the composite figure into its individual rectangles.
The area of a rectangle is given by length x width. Let the height of the larger rectangle be x meters.
The area of the smaller rectangle is 4m x 3m = 12 square meters.
The area of the larger rectangle is (8m x x) - (4m x 3m) = 8x - 12 square meters.
Given that the area of the composite figure is 52 square meters, we have:
12 + 8x - 12 = 52
8x = 52
8x = 52
x = 6.5
Therefore, the value in meters of the height of the larger rectangle is 6.5 meters.