Question

The Ward family is redecorating several rooms of their house. angelique wants to have a rug that is 9 feet long and 7 feet wide in her bedroom. the rug will cover the whole floor except a border that is x feet wide. the area of her room is 167 square feet. find the width of the border, x. round the answer to the nearest tenth of a foot.

Answer 1

The width of the border will be about 2.5 feet.

The area of the rug is 9 by 7. Let's call the width of the border x. Therefore, the length of the rug will switch to 9 + 2x. The border is on both sides of it, so we add on 2x. Then, the width is 7 + 2x.

The area of the room is therefore: (9 + 2x)(7+ 2x).

We know the area of the room, so we can write and solve the following equation.

(9 + 2x)(7 + 2x) = 167
4x^2 + 32x + 63 = 167
4x^2 + 32x - 107 = 0

At this point, use the quadratic formula and x will equal about 2.5.