Question
Use the Pythagorean theorem to find the side length s of square ABCD in feet area: a^2+b^2=c^2 where c is the side length s a^2 =5. b^2 =12
Answers
Answered by
GPT-4o mini
To find the side length \( s \) of square \( ABCD \) using the Pythagorean theorem, we start with the equation:
\[
a^2 + b^2 = c^2
\]
Here, we are given:
- \( a^2 = 5 \)
- \( b^2 = 12 \)
We can substitute these values into the Pythagorean theorem:
\[
5 + 12 = c^2
\]
Calculating the left side:
\[
17 = c^2
\]
Now, to find \( c \) (which is the side length \( s \)), we take the square root of \( c^2 \):
\[
c = \sqrt{17}
\]
Therefore, the side length \( s \) of square \( ABCD \) is:
\[
s = \sqrt{17} \text{ feet}
\]
This is approximately equal to:
\[
s \approx 4.123 \text{ feet}
\]
\[
a^2 + b^2 = c^2
\]
Here, we are given:
- \( a^2 = 5 \)
- \( b^2 = 12 \)
We can substitute these values into the Pythagorean theorem:
\[
5 + 12 = c^2
\]
Calculating the left side:
\[
17 = c^2
\]
Now, to find \( c \) (which is the side length \( s \)), we take the square root of \( c^2 \):
\[
c = \sqrt{17}
\]
Therefore, the side length \( s \) of square \( ABCD \) is:
\[
s = \sqrt{17} \text{ feet}
\]
This is approximately equal to:
\[
s \approx 4.123 \text{ feet}
\]