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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Let's find the dimensions of both rectangles first.
The top rectangle has a length of 3 meters and a width of 4 meters.
The bottom rectangle has a width of 8 meters.
The area of the composite figure is the sum of the areas of both rectangles.
Let's denote the height of the larger rectangle as "h".
The area of the top rectangle is 3 meters x 4 meters = 12 square meters.
The area of the bottom rectangle is 8 meters x h meters = 8h square meters.
The total area of the composite figure is 12 square meters + 8h square meters = 52 square meters.
12 + 8h = 52
8h = 40
h = 5
Therefore, the height of the larger rectangle is 5 meters.