Question
Find the length of side a.
An image displaying a right angled triangle with two legs equals a units and 5 units and hypotenuse equals 13 units.
A.
144
B.
C.
12
D.
8
An image displaying a right angled triangle with two legs equals a units and 5 units and hypotenuse equals 13 units.
A.
144
B.
C.
12
D.
8
Answers
GPT-4o mini
To find the length of side \( a \) in a right-angled triangle where one leg is \( a \), the other leg is \( 5 \), and the hypotenuse is \( 13 \), we can use the Pythagorean theorem:
\[
a^2 + b^2 = c^2
\]
Here, \( b = 5 \) and \( c = 13 \), so we plug in the values:
\[
a^2 + 5^2 = 13^2
\]
Calculating \( 5^2 \) and \( 13^2 \):
\[
a^2 + 25 = 169
\]
Next, we can solve for \( a^2 \):
\[
a^2 = 169 - 25
\]
\[
a^2 = 144
\]
Now, take the square root of both sides to find \( a \):
\[
a = \sqrt{144} = 12
\]
Therefore, the length of side \( a \) is \( 12 \).
Thus, the correct answer is:
**C. 12**
\[
a^2 + b^2 = c^2
\]
Here, \( b = 5 \) and \( c = 13 \), so we plug in the values:
\[
a^2 + 5^2 = 13^2
\]
Calculating \( 5^2 \) and \( 13^2 \):
\[
a^2 + 25 = 169
\]
Next, we can solve for \( a^2 \):
\[
a^2 = 169 - 25
\]
\[
a^2 = 144
\]
Now, take the square root of both sides to find \( a \):
\[
a = \sqrt{144} = 12
\]
Therefore, the length of side \( a \) is \( 12 \).
Thus, the correct answer is:
**C. 12**