Question
What is the length of the missing leg in this right triangle?
A right triangle has a side with length 7 millimeters and hypotenuse with length 25 millimeters.
18 mm
24 mm
26 mm
32 mm
A right triangle has a side with length 7 millimeters and hypotenuse with length 25 millimeters.
18 mm
24 mm
26 mm
32 mm
Answers
GPT-4o mini
To find the length of the missing leg in a right triangle, we can use the Pythagorean theorem, which states:
\[
a^2 + b^2 = c^2
\]
where \( c \) is the length of the hypotenuse, and \( a \) and \( b \) are the lengths of the other two sides. In this case, we know one leg \( a \) is 7 mm, and the hypotenuse \( c \) is 25 mm. We need to find the length of the other leg \( b \).
Plugging in the known values:
\[
7^2 + b^2 = 25^2
\]
Calculating \( 7^2 \) and \( 25^2 \):
\[
49 + b^2 = 625
\]
Now, we subtract 49 from both sides:
\[
b^2 = 625 - 49
\]
\[
b^2 = 576
\]
Next, we take the square root of both sides to find \( b \):
\[
b = \sqrt{576}
\]
\[
b = 24
\]
Thus, the length of the missing leg is **24 millimeters**.
\[
a^2 + b^2 = c^2
\]
where \( c \) is the length of the hypotenuse, and \( a \) and \( b \) are the lengths of the other two sides. In this case, we know one leg \( a \) is 7 mm, and the hypotenuse \( c \) is 25 mm. We need to find the length of the other leg \( b \).
Plugging in the known values:
\[
7^2 + b^2 = 25^2
\]
Calculating \( 7^2 \) and \( 25^2 \):
\[
49 + b^2 = 625
\]
Now, we subtract 49 from both sides:
\[
b^2 = 625 - 49
\]
\[
b^2 = 576
\]
Next, we take the square root of both sides to find \( b \):
\[
b = \sqrt{576}
\]
\[
b = 24
\]
Thus, the length of the missing leg is **24 millimeters**.