Question

Cynthia Besch wants to buy a rug for a room that is 1919 ft wide and 2727 ft long. She wants to leave a uniform strip of floor around the rug. She can afford to buy 153153 square feet of carpeting. What dimensions should the rug​ have?

Answer 1

Answer:

The dimension of the rug would be 17 ft × 9 ft.

Step-by-step explanation:

Given

length of the room = 27 ft.

width of the room = 19 ft.

suppose, she leaves a uniform strip of x ft. around the rug.

So,

The length of rug = (27-2x)ft.

Width of rug= (19-2x)ft.

∴ Area of the rug= length×width

                            $= (27-2x)(19-2x)$

                            $= 513-54x-38x+4x^2$

                            $= 513-92x+4x^2$

According to the question,

$513-92x+4x^2=153$

$513-92x+4x^2-153=0$        ( subtract 153 both sides)

$4x^2-92x+360=0$

$4(x^2-23x+90)=0$

$x^2-23x+90=0$

$x^2-(18+5)x+90=0$            ( Middle term splitting)

$x^2-18x-5x+90=0$

$x(x-18)-5(x-18)=0$

$(x-5)(x-18)=0$

$x-5=0$ or $x-18=0$             ( zero product property)

$x=5$ or $x=18$

if x=18, dimension would be negative  ( Not possible)

Thus, x= 5

Hence,

length of rug= 27-10=17 ft.

width of rug= 19-10=9 ft.