Question
Find the missing side length.
Right triangle with side length 12 and hypotenuse length 13.
Responses
18
18
25
25
5
5
17.7
Right triangle with side length 12 and hypotenuse length 13.
Responses
18
18
25
25
5
5
17.7
Answers
Answered by
GPT-4o mini
To find the missing side length of a right triangle with one side length of 12 and a hypotenuse length of 13, we can use the Pythagorean theorem:
\[
a^2 + b^2 = c^2
\]
where \(c\) is the hypotenuse and \(a\) and \(b\) are the two other sides. We can assign \(a = 12\) and \(c = 13\). We need to find the length of side \(b\).
Using the Pythagorean theorem, we plug in the values:
\[
12^2 + b^2 = 13^2
\]
Calculating the squares:
\[
144 + b^2 = 169
\]
Now, subtract 144 from both sides:
\[
b^2 = 169 - 144
\]
\[
b^2 = 25
\]
Taking the square root of both sides gives:
\[
b = \sqrt{25} = 5
\]
The missing side length is \(5\).
Among the responses provided, the correct answer is:
**5**
\[
a^2 + b^2 = c^2
\]
where \(c\) is the hypotenuse and \(a\) and \(b\) are the two other sides. We can assign \(a = 12\) and \(c = 13\). We need to find the length of side \(b\).
Using the Pythagorean theorem, we plug in the values:
\[
12^2 + b^2 = 13^2
\]
Calculating the squares:
\[
144 + b^2 = 169
\]
Now, subtract 144 from both sides:
\[
b^2 = 169 - 144
\]
\[
b^2 = 25
\]
Taking the square root of both sides gives:
\[
b = \sqrt{25} = 5
\]
The missing side length is \(5\).
Among the responses provided, the correct answer is:
**5**