Question

Answer each of the following items. Show relevant and neat solutions. 1. Town A is 33 kilometers from the main highway, and Town B is 16 kilometers from that same highway. Their roads are 119 kilometers apart. A developer wants to build a mall along that highway and connecting roads that go directly from the mall to the two towns. Where should he place the mall so that it's the same distance from each town? (4 points) Display Settings United States)

Answer 1

Answer:

56 Km from road A

Step-by-step explanation:

The situation is depicted in the picture attached.

By the Pythagorean Theorem

$x^2=33^2+y^2$ and

$x^2=16^2+(119-y)^2$

hence

$33^2+y^2= 16^2+(119-y)^2$

solving the equation:

$1089+y^2=256+14161-238y+y^2$

$1089=14417-238y$

and

y = 56 Km

So the developer should place the mall 56 Km from the road  

the intersection of Town A road and the highway.