Question

1. what is the length of the hypotenuse of the triangle when $x = 2$?

$4x + 4$
$3x - 1$

Explanation:

Step1: Find the lengths of the legs

First, we substitute \( x = 2 \) into the expressions for the legs of the right triangle.
For the vertical leg: \( 4x + 4 \), substitute \( x = 2 \):
\( 4(2) + 4 = 8 + 4 = 12 \)
For the horizontal leg: \( 3x - 1 \), substitute \( x = 2 \):
\( 3(2) - 1 = 6 - 1 = 5 \)

Step2: Use the Pythagorean theorem

The Pythagorean theorem states that for a right triangle with legs \( a \) and \( b \), and hypotenuse \( c \), \( c = \sqrt{a^2 + b^2} \).
Here, \( a = 12 \) and \( b = 5 \), so we calculate:
\( c = \sqrt{12^2 + 5^2} = \sqrt{144 + 25} = \sqrt{169} = 13 \)

Answer:

13