Question

what is the length of the hypotenuse of the triangle when x = 2?
the length of the hypotenuse is \\(\square\\) unit(s)
(type an integer or decimal rounded to the nearest tenth as needed)
(the image shows a right triangle with legs labeled \\(3x + 6\\) and \\(6x - 3\\))

Explanation:

Step1: Substitute \( x = 2 \) into the legs' expressions

For the first leg: \( 3x + 6 = 3(2) + 6 = 6 + 6 = 12 \)
For the second leg: \( 6x - 3 = 6(2) - 3 = 12 - 3 = 9 \)

Step2: Apply the Pythagorean theorem (\( c = \sqrt{a^2 + b^2} \))

Let \( a = 12 \), \( b = 9 \). Then \( c = \sqrt{12^2 + 9^2} = \sqrt{144 + 81} = \sqrt{225} = 15 \) (Wait, actually, \( 12^2 + 9^2 = 144 + 81 = 225 \), and \( \sqrt{225}=15 \). But maybe I misread the legs? Wait, no, if \( x=2 \), 3x+6=12, 6x-3=9. Then hypotenuse is \( \sqrt{12^2 + 9^2} = 15 \). Wait, but maybe the triangle is right-angled, so Pythagorean theorem applies.

Wait, maybe I made a mistake? Let's check again. 3x+6 when x=2: 32=6, 6+6=12. 6x-3: 62=12, 12-3=9. Then \( 12^2 + 9^2 = 144 + 81 = 225 \), square root of 225 is 15. So the hypotenuse is 15.

Answer:

15