Question

Which of the following represents the dimensions of the room

Answer 1

Given:

The length of the rectangular room is 6 more than the width.

The area of the room, A = 27 square units.

Required:

We need to find the dimensions of the given rectangular room.

Step-by-step explanation:

Let w be the width of the rectangle.

6 more than means add 6.

The length of the rectangle, l= w+6.

Consider the area of the rectangle formula.

`A=lw`

Substitute A = 27, and l=w+6 in the formula.

`27=(w+6)w`

`27=w^2+6w`

Subtract 27 from both sides of the equation.

`27-27=w^2+6w-27`

`0=w^2+6w-27`

`w^2+6w-27=0`
`Use\text{ }6w=9w-3w.`

`w^2+9w-3w-27=0`

Take out the common multiple.

`w(w+9)-3(w+9)=0`

`(w+9)(w-3)=0`

`(w+9)=0,(w-3)=0`
`w=-9,3`

The measure is always positive.

`w=3\text{ units,}`

Substitute w =3 in the equation l =w+6.

`l=3+6=9\text{ units.}`

We get l =9 units and w =3 units.

Final answer:

The dimensions of the room are 3 and 9.