Question

what is the length of side x?
13
5
x
select the best answer

Explanation:

Step1: Identify the triangle type

The triangle is a right triangle (has a right angle, marked by the red square). So we can use the Pythagorean theorem, which states that for a right triangle with hypotenuse \( c \) and legs \( a \), \( b \), \( a^{2}+b^{2}=c^{2} \). Here, hypotenuse \( c = 13 \), one leg \( b = 5 \), and the other leg is \( x \) (we'll call it \( a \)).

Step2: Apply the Pythagorean theorem

Substitute the known values into the formula: \( x^{2}+5^{2}=13^{2} \). Calculate \( 5^{2}=25 \) and \( 13^{2}=169 \). So the equation becomes \( x^{2}+25 = 169 \).

Step3: Solve for \( x^{2} \)

Subtract 25 from both sides: \( x^{2}=169 - 25 \). \( 169-25 = 144 \), so \( x^{2}=144 \).

Step4: Solve for \( x \)

Take the square root of both sides. Since length can't be negative, we take the positive square root: \( x=\sqrt{144}=12 \).

Answer:

12