Area of the larger rectangle = 40 square meters

Question

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?

Answer 1

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.