Question

City A is 10 miles from city B and 5 miles from city C. Cities A, B, and C form a right triangle at A. A road connects cities B and C directly. Find the length of this road.

Answer 1

11.18 miles

Explanation:

The sides of a right triangle a, b, c are related by the equation

a^2 + b^2 = c^2

where c is the longest side of the triangle

Hence given that A connects B and C directly and forms a right angle at A

5^2 + 10^2 = c^2

Where c is the length of the road

25 + 100 = c^2

125 = c^2

c = 125^1/2

= 11.18 miles