In the triangular prism, the length of JE is 12 inches, the length of EF is 3 inches, and the length of FG is 4 inches.
Note: Image not drawn to scale.
What is the length of a line segment drawn from point J to point G?
A. 7 inches
B. 5 inches
C. 13 inches
D. 17 inches
To find the length of a line segment drawn from point J to point G, we can use the Pythagorean Theorem since JG is the hypotenuse of a right triangle.
First, we need to find the lengths of the other two sides of the triangle. We have EF = 3 inches and FG = 4 inches.
Using the Pythagorean Theorem:
(JF)^2 = (EF)^2 + (FG)^2
(JF)^2 = 3^2 + 4^2
(JF)^2 = 9 + 16
(JF)^2 = 25
JF = sqrt(25)
JF = 5 inches
Now, we have the lengths of JE = 12 inches and JF = 5 inches, we can use the Pythagorean Theorem again:
(JG)^2 = (JE)^2 + (JF)^2
(JG)^2 = 12^2 + 5^2
(JG)^2 = 144 + 25
(JG)^2 = 169
JG = sqrt(169)
JG = 13 inches
Therefore, the length of a line segment drawn from point J to point G is 13 inches.
The correct answer is C. 13 inches.