Question

A rug is to be centered in a room so that the border around it is of a consistent width on all four sides. If the room is 10 ft by 15 ft, and the area of the rug is 24 square feet, how wide will the border be?

Answer 1

The width of the border can be 9 feet or 3.5 feet.

Explanation:

Let the width be x

Length of room = 10 feet

Breadth of room = 15 feet

Length of rug = 10-2x

Breadth of rug = 15-2x

Area of rug =
`(10-2x)(15-2x)`

We are given that the area of the rug is 24 square feet.

So,
`(10-2x)(15-2x)=24` ---A

`150-20x-30x+4x^2=24`

`150-24-50x+4x^2=0`

`126-50x+4x^2=0`

`2(x-9)(2x-7)=0`

`x=9,(7)/(2)`

`x=9,3.5`

Substitute x =9 in A

`(10-2(9))(15-2(9))=24`

`24=24`

LHS = RHS

Substitute x = 3.5

`(10-2(3.5))(15-2(3.5))=24`

`24=24`

LHS = RHS

So, The width of the border can be 9 feet or 3.5 feet.