Question
What is the length of the unknown side of the right triangle?
14, 7, a
(1 point)
Responses
147−−−√ ft.
147−−−√ ft.
14−−√ ft.
14−−√ ft.
7 ft.
7 ft.
21 ft.
14, 7, a
(1 point)
Responses
147−−−√ ft.
147−−−√ ft.
14−−√ ft.
14−−√ ft.
7 ft.
7 ft.
21 ft.
Answers
GPT-4o mini
To find the length of the unknown side \( a \) in the right triangle with the other two sides being 14 ft and 7 ft, we can use the Pythagorean theorem, which states:
\[
a^2 + b^2 = c^2
\]
where \( c \) is the hypotenuse.
Assuming \( 14 \) ft is the hypotenuse, and \( 7 \) ft is one of the legs, we can substitute:
\[
7^2 + a^2 = 14^2
\]
Calculating \( 7^2 \) and \( 14^2 \):
\[
49 + a^2 = 196
\]
Subtract \( 49 \) from both sides:
\[
a^2 = 196 - 49
\]
\[
a^2 = 147
\]
Taking the square root of both sides to find \( a \):
\[
a = \sqrt{147}
\]
Thus, the length of the unknown side \( a \) is:
\[
\sqrt{147} \text{ ft.}
\]
So the correct response is:
\(\sqrt{147} \text{ ft.}\)
\[
a^2 + b^2 = c^2
\]
where \( c \) is the hypotenuse.
Assuming \( 14 \) ft is the hypotenuse, and \( 7 \) ft is one of the legs, we can substitute:
\[
7^2 + a^2 = 14^2
\]
Calculating \( 7^2 \) and \( 14^2 \):
\[
49 + a^2 = 196
\]
Subtract \( 49 \) from both sides:
\[
a^2 = 196 - 49
\]
\[
a^2 = 147
\]
Taking the square root of both sides to find \( a \):
\[
a = \sqrt{147}
\]
Thus, the length of the unknown side \( a \) is:
\[
\sqrt{147} \text{ ft.}
\]
So the correct response is:
\(\sqrt{147} \text{ ft.}\)