Geometry finding the sides of an angle

Question

The perimeter of triangle uvw is 22.5 and wz bisects angle uwv uz = 2 and vz =2.5 find uw and vw

Answer 1

Hello Nancy;

Firstly, |UW| + |VW| + 2 + 2.5 = 22.5

|UW| + |VW| = 18...........(1)

Using bisector relation;

|UW| / 2 = |VW| /2.5........(2)

Solving two equations simultaneously we find

|UW| = 8

|VW| = 10