Question
The width of a rectangle is 5 inches, and the diagonal length of the rectangle is 25 inches. Which measurement is closest to the length of this rectangle in inches?
Responses
A 625 inches625 inches
B 600 inches600 inches
C 34.5 inches34.5 inches
D 24.5 inches
Responses
A 625 inches625 inches
B 600 inches600 inches
C 34.5 inches34.5 inches
D 24.5 inches
Answers
GPT-4o mini
To find the length of the rectangle given the width and the length of the diagonal, we can use the Pythagorean theorem. The formula is:
\[
a^2 + b^2 = c^2
\]
where \( a \) is the width, \( b \) is the length, and \( c \) is the diagonal.
In this case:
- Width (\( a \)) = 5 inches
- Diagonal (\( c \)) = 25 inches
We need to find the length (\( b \)). Rearranging the equation gives us:
\[
b^2 = c^2 - a^2
\]
Substituting the known values:
\[
b^2 = 25^2 - 5^2
\]
\[
b^2 = 625 - 25
\]
\[
b^2 = 600
\]
Now, taking the square root of both sides:
\[
b = \sqrt{600}
\]
\[
b \approx 24.49 \text{ inches}
\]
Thus, the length of the rectangle is approximately 24.5 inches.
The closest measurement from the options provided is:
**D 24.5 inches**.
\[
a^2 + b^2 = c^2
\]
where \( a \) is the width, \( b \) is the length, and \( c \) is the diagonal.
In this case:
- Width (\( a \)) = 5 inches
- Diagonal (\( c \)) = 25 inches
We need to find the length (\( b \)). Rearranging the equation gives us:
\[
b^2 = c^2 - a^2
\]
Substituting the known values:
\[
b^2 = 25^2 - 5^2
\]
\[
b^2 = 625 - 25
\]
\[
b^2 = 600
\]
Now, taking the square root of both sides:
\[
b = \sqrt{600}
\]
\[
b \approx 24.49 \text{ inches}
\]
Thus, the length of the rectangle is approximately 24.5 inches.
The closest measurement from the options provided is:
**D 24.5 inches**.