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 value in meters of the height of the larger rectangle, we can use the formula for the area of a rectangle:
Area = length * width
In this case, we are given that the area of the composite figure is 52 square meters. Let's call the length of the larger rectangle L and the width W.
The larger rectangle can be divided into two parts: the top rectangle (smaller rectangle) and the bottom rectangle.
The area of the top rectangle (smaller rectangle) is given as 4 meters * 3 meters = 12 square meters.
The area of the bottom rectangle is then the total area of the larger rectangle minus the area of the top rectangle:
Area of bottom rectangle = 52 square meters - 12 square meters = 40 square meters.
Using the formula for the area of a rectangle, we have:
40 square meters = L * 8 meters
Simplifying the equation, we have:
L = 40 square meters / 8 meters = 5 meters.
Therefore, the height of the larger rectangle is 5 meters.