Area of the larger rectangle = 40 square meters
Area of the smaller rectangle = 12 square meters
The area of the composite figure is 52 square meters. What is the value in meters of the height of the larger rectangle?
Let's denote the height of the larger rectangle as h and the width as w.
Given:
Area of the larger rectangle = h * w = 40 square meters
Area of the smaller rectangle = 12 square meters
We also know that the total area of the composite figure is equal to the sum of the areas of the two rectangles:
40 + 12 = h * w + 12
52 = h * w + 12
Since we are looking for the height of the larger rectangle, we can express the width of the larger rectangle in terms of its height:
w = 40 / h
Now we can substitute w in the equation for the total area of the composite figure:
52 = h * (40/h) + 12
52 = 40 + 12
52 = 52
Now we can solve for h:
52 = 52
Therefore, the value of the height of the larger rectangle is 40 meters.