Pleasee help. "A rug is needed to cover 2 thirds of the area of a room with dimensions 8 x 12. The uncovered part of the floor will form a border of uniform width around the rug. Determine the width of the border.

Thanks so much !!!!!!!!!!

Question

Pleasee help. "A rug is needed to cover 2 thirds of the area of a room with dimensions 8 x 12. The uncovered part of the floor will form a border of uniform width around the rug. Determine the width of the border.

Thanks so much !!!!!!!!!!

anonymous · Answer

|dw:1318136923002:dw|
area of room=96
area of rug=64

64=(8-2x)(12-2x)
4x^2-40x+32=0
x^2-10x+8=0
x^2-10x+25=-8+25
(x-5)^2=17
x=5 + sqrt{17}
this is the width of the border around the rug