Answer is 16 ft x 26 ft carpet
Step by step
First we know the room is 24 x 34
We know the carpet area is 416 sq ft
We know there will be an equal strip of floor not covered by carpet
Since the area of carpet is 416 sq ft, and area is L x W, I found the factors of 416 are 1, 2, 4, 8, 13, 16, 26, 32, 52, 104, 208, 416.
16 x 26 = 416
The room dimensions are 24 x 34
24’ room - 16’ carpet = 8’
34’ room - 26’ carpet = 8’
So there will be an 8 ft strip around the edge of the room
with carpet measurements of 16’ x 26’
Problem solved!
