jmc

Question

Piravena must make a trip from A to B, then from B to C, then from C to A. Each of these three parts of the trip is made entirely by bus or entirely by airplane. The cities form a right-angled triangle as shown, with C a distance of 3000 km from A and with B a distance of 3250 km from A. To take a bus, it costs Piravena 0.15 per kilometer. To take an airplane, it costs her a 100 booking fee, plus 0.10$ per kilometer. FIGURE Determine the distance she travels for her complete trip.

Accepted Answer

Since ABC is a right-angled triangle, then we may use the Pythagorean Theorem. Thus, AB^2=BC^2+CA^2, and so align* BC^2&=AB^2-CA^2 &=3250^2-3000^2 &=250^2(13^2-12^2) &=250^2(5^2) &=1250^2. align* therefore BC=1250 km (since BC>0). Piravena travels a distance of 3250+1250+3000=7500 km for her complete trip.