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)
the height of the larger rectangle is 5
u sure
To find the height of the larger rectangle, we need to find the total height of the composite figure.
The total height of the composite figure can be calculated by adding the height of the smaller rectangle (3 meters) and the distance between the top and bottom rectangles (2 meters).
3 meters + 2 meters = 5 meters
Since the area of the composite figure is given as 52 square meters, we can use the formula for finding the area of a rectangle:
Area = length x width
We know the width of the larger rectangle is 8 meters, and we just calculated the total height as 5 meters. Let's assign the height of the larger rectangle as 'x'.
So, we have the equation:
8 meters x x = 52 square meters
Solving for x:
8x = 52
x = 52 / 8
x = 6.5
Therefore, the value in meters of the height of the larger rectangle is 6.5 meters.
Apologies for the mistake in my calculation. Let's correct that.
We have previously determined that the total height of the composite figure is 5 meters. We also know that the total width of the composite figure is 8 meters, which is the width of the larger rectangle.
To find the area of the composite figure, we can use the formula for the area of a rectangle, which is length x width. Given that the area of the composite figure is 52 square meters, we can set up the following equation:
5 meters x 8 meters = 52 square meters
40 square meters = 52 square meters
This is incorrect and indicates an error in my previous explanation. Let's try a different approach to solve this:
Let the height of the larger rectangle be 'x' meters. On adding the height of the smaller rectangle (3 meters) and the distance between the rectangles (2 meters), we get the total height of the composite figure as 5 meters. This means:
3 meters (height of the smaller rectangle) + x meters (height of the larger rectangle) = 5 meters
x = 5 - 3
x = 2 meters
Therefore, the height of the larger rectangle is 2 meters.