The area of the composite figure is 52 square meters.
What is the value in meters of the height of the larger rectangle?
In order to determine the height of the larger rectangle, we need to break down the composite figure into its individual shapes.
Let's assume that the composite figure is made up of two rectangles: a larger rectangle and a smaller rectangle on top of it.
Let the longer side of the larger rectangle be x meters and let the height of the smaller rectangle (which is the same as the width of the larger rectangle) be y meters.
The area of the larger rectangle is xy and the area of the smaller rectangle is xy/2.
Given that the total area of the composite figure is 52 square meters, we have the equation xy + xy/2 = 52.
Combining like terms, we get 3xy/2 = 52.
To find the value of x, we need to consider that y = x/2 (since the smaller rectangle's height is half that of the larger rectangle's width).
Substitute y = x/2 into the equation 3xy/2 = 52:
3(x)(x/2)/2 = 52
3x^2/4 = 52
3x^2 = 208
x^2 = 208/3
x ≈ 5.68 meters
Therefore, the value of the height of the larger rectangle is approximately 5.68 meters.