Question

The area of the green square is 9 . The area of the red square is 16 .

What is the length of side c?
Responses

A 5 ft5 ft

B 25 ft25 ft

C 81 ft81 ft

D 128 ft128 ft

E 256 ft

Answer 1

To find the side lengths of the squares, we can take the square root of their areas.

1. For the green square with area 9:
\[
\text{Side length of green square} = \sqrt{9} = 3 \text{ ft}
\]

2. For the red square with area 16:
\[
\text{Side length of red square} = \sqrt{16} = 4 \text{ ft}
\]

The problem refers to side length \(c\), but it does not specify exactly what \(c\) represents in relation to the squares. However, given the options provided, if we assume \(c\) represents the total side length when both squares are put together or one of the notable derived values, we can consider:

If \(c\) were representing the sum of the side lengths:
\[
c = 3 + 4 = 7 \text{ ft} \;(\text{which is not an option provided})
\]

If \(c\) were representing the area (as calculated previously):
- Area of the green square = 9
- Area of the red square = 16

The total area would be:
\[
c = 9 + 16 = 25 \text{ ft}^2 \;(\text{which is the square of 5 ft})
\]

If we're looking for length \(c\), representing the geometric relationship in terms of total area or dimensions:
\[
c = \sqrt{25} = 5 \text{ ft}
\]
Option A matches this conclusion.

Thus, the most appropriate response for the length of side \(c\) is:
**A 5 ft**.