A rug is to fit in a room so that a border of even width is left on all four sides. If the room is 12 feet by 15 feet and the area of the rug is 108 square feet, how wide will the border be?

Question

A rug is to fit in a room so that a border of even width is left on all four sides. If the room is 12 feet by 15 feet and the area of the rug is 108 square feet, how wide will the border be?

2 Answers

Answer Question

Answer 1

You can write a quadratic equation, or you can estimate, or you can make an educated guess.
108 = 1*108 = 2*54 = 3*36 = 4*27 = 6*18 = 9*12
The dimensions 9 by 12 are each 3 ft less than the dimensions 12 by 15. The border will be half of 3 ft, that is 1.5 ft.
_____
The perimeter of the room is 2(12+15)=54 ft. The difference between the area of the room and the area of the rug is 180 ft^2 - 108 ft^2 = 72 ft^2, so the width of the border can be estimated as slightly more than 72ft^2/(54ft), about 1.5 ft.

Answer 2

Good afternoon! For what purpose do you need such precise calculations? Do you want to fit the rug in a certain place or do you want to save money? I mean, I recently bought antique rugs for my house and it was pretty cheap. So if you're worried about the cost, I'm sure you'll be fine with that price.