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 first need to find the width of the larger rectangle. The width of the larger rectangle can be calculated by adding the width of the smaller rectangle (3 meters) to the distance between the right side of the smaller rectangle and the right side of the larger rectangle (2 meters):
Width = 3 meters + 2 meters = 5 meters
Next, we can calculate the area of the larger rectangle using the width we just found and the total area of the composite figure:
Area of larger rectangle = Total area - Area of smaller rectangle
Area of larger rectangle = 52 square meters - (3 meters * 4 meters) = 52 square meters - 12 square meters = 40 square meters
Finally, we can find the height of the larger rectangle by dividing the area of the larger rectangle by the width of the larger rectangle:
Height of larger rectangle = Area of larger rectangle / Width
Height of larger rectangle = 40 square meters / 5 meters = 8 meters
Therefore, the height of the larger rectangle is 8 meters.