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Answer:
5km
Step-by-step explanation:
Pythagorean Theorem
[tex] a^2 + b^2 = c^2 [/tex]
(a and b are the legs, c is the hypotenuse)
If you will draw four lines to represent the direction of North, South, East, and West, you can easily see that if he went 4km due east then 3km due north, this resembles a right triangle with legs measuring 4km and 3km.
[tex] c^2 = 4^2 + 3^2 [/tex]
[tex] c^2 = 16 + 9 [/tex]
[tex] c^2 = 25 [/tex]
[tex] c = \sqrt{25} [/tex]
[tex] c = 5 [/tex]
Therefore, John is 5km away from his house.