Question

The length of a rectangular storage room is 3 feet longer than its width. if the area of the room is 40 square feet, find the width.

Answer 1

Width of rectangular storage room= 5 feet.

Explanation:

Let x be the width of storage room.

We have been given that the length of a rectangular storage room is 3 feet longer than its width. So the length of storage room will be x+3.

We are also given that the area of the room is 40 square feet.

Since the area of a rectangle is length times width.

`\text{Area of rectangle}=\text{Length* Width}`

Let us substitute our given values in area formula.

`40=x*(x+3)`

Upon distributing x we will get,

`40=x^2+3x`

`x^2+3x-40=0`

Now let us factor out our quadratic equation using splitting the middle term.

`x^2+8x-5x-40=0`

`x(x+8)-5(x+8)=0`

`(x+8)(x-5)=0`

`x+8=0` or
`x-5=0`

`x=-8` or
`x=5`

Since width can not be negative, therefore, the width of rectangle will be 5 feet.

Let us verify our answer.

Length of rectangular storage room is 3 feet longer than its width. So length will be 5+3=8.

Given: Area=40 square feet.

5*8=40.

Hence, width of rectangular storage room is 5 feet.