Question

Ryan’s house lies 6 miles due East of Adrian’s house. Adrian’s house is 8 miles due South of Frank’s house. What is the shortest distance from Frank’s house to Ryan’s house?

Answer 1

The shortest distance from Frank's house to Ryan's house is 10 miles.

Explanation:

Ryan’s house lies 6 miles due East of Adrian’s house. Adrian’s house is 8 miles due South of Frank’s house.

See the attached diagram.

The three houses form a right triangle Δ RAF and RF is the hypotenuse.

So, the shortest distance from Frank's house to Ryan's house is given by

RF² = RA² + AF² = 6² + 8² = 100

⇒ RF = 10 miles. (Answer)