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 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 area of the composite figure is 52 square meters. What is the value in meters of the height of the larger rectangle?
(1 point)
Answers
Answered by
GPT-4o mini
To find the height of the larger rectangle, we first need to understand the relationship between the two rectangles and the total area provided.
Let's denote:
- The width of the larger rectangle as \( W \).
- The height of the larger rectangle as \( H \).
- The width of the smaller rectangle as \( w \).
- The height of the smaller rectangle as \( h \).
The area of the larger rectangle is given by:
\[
A_{\text{large}} = W \times H
\]
The area of the smaller rectangle is given by:
\[
A_{\text{small}} = w \times h
\]
The total area of the composite figure is the sum of the areas of the two rectangles:
\[
A_{\text{composite}} = A_{\text{large}} + A_{\text{small}} = W \times H + w \times h
\]
According to the problem, the total area \( A_{\text{composite}} \) is 52 square meters:
\[
W \times H + w \times h = 52
\]
However, without additional information about the dimensions of the smaller rectangle (\( w \) and \( h \)) or the dimensions of the larger rectangle (\( W \) and \( H \)), we cannot determine the exact height \( H \) of the larger rectangle.
To provide a specific numerical answer or further information, more details on the dimensions or relationships between the rectangles would be necessary. If you have any specific values or conditions for \( W \), \( H \), \( w \), or \( h \), please share them, and I can provide a more precise answer.
Let's denote:
- The width of the larger rectangle as \( W \).
- The height of the larger rectangle as \( H \).
- The width of the smaller rectangle as \( w \).
- The height of the smaller rectangle as \( h \).
The area of the larger rectangle is given by:
\[
A_{\text{large}} = W \times H
\]
The area of the smaller rectangle is given by:
\[
A_{\text{small}} = w \times h
\]
The total area of the composite figure is the sum of the areas of the two rectangles:
\[
A_{\text{composite}} = A_{\text{large}} + A_{\text{small}} = W \times H + w \times h
\]
According to the problem, the total area \( A_{\text{composite}} \) is 52 square meters:
\[
W \times H + w \times h = 52
\]
However, without additional information about the dimensions of the smaller rectangle (\( w \) and \( h \)) or the dimensions of the larger rectangle (\( W \) and \( H \)), we cannot determine the exact height \( H \) of the larger rectangle.
To provide a specific numerical answer or further information, more details on the dimensions or relationships between the rectangles would be necessary. If you have any specific values or conditions for \( W \), \( H \), \( w \), or \( h \), please share them, and I can provide a more precise answer.