floor of aroom is8mby 5m .area of border of carpet is 12 m squared.find width of border.

if border has width w,

40-(8-2w)(5-2w) = 12
w = 1/2

A carpet is placed in a hall leaving border of 2m wide all around the room. If the room is 18mlong and 12m wide find the area uncovered by the carpet?

To find the width of the border, we need to consider that the area of the carpet is equal to the difference between the area of the room and the area of the floor.

The area of the room's floor is given as 8m by 5m, which equals 8 * 5 = 40 square meters.

Let's assume the width of the border is "x" meters.

To find the area of the border, we can subtract the area of the floor from the total area of the carpet:

Area of the border = Area of the carpet - Area of the floor

Given that the area of the border is 12 square meters, we can set up the equation:

12 = (8 + 2x)(5 + 2x) - 40

Expanding this equation, we get:

12 = (40 + 16x + 10x + 4x^2) - 40

Simplifying further, we have:

12 = 16x + 10x + 4x^2

Rearranging the terms, we get a quadratic equation:

4x^2 + 26x - 12 = 0

To solve this quadratic equation, we can use factoring, completing the square, or the quadratic formula.

Once we solve for "x," we will find the width of the border.