Question

The width of a rectangle is the length minus 6 units. The area of the rectangle is 27 units. What is the length, in units, of the rectangle.

Answer 1

9

Explanation:

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Answer 2

`Length=9\,\,units`

Explanation:

Let, the length of the rectangle be 'L'

Width of the rectangle be 'W'

`Width=Length-6\\\\W=L-6`

Area of the rectangle=
`27\,\,units`

Area of a rectangle=
`Length* Width`

`27=Length* Width`

`27=L* (L-6)`

`L^2-6L=27\\\\L^2-6L-27=0`

`L^2+3L-9L-27=0\\\\ L(L+3)-9(L+3)=0\\\\(L+3)(L-9)=0\\\\`

Equating to zero:

`L+3=0\\L=-3`

OR, Similarly:

`L=9` units

The length of the rectangle cannot be negative,

therefore,

`Length=9\,\,units`

`W=L-6\\\\W=9-6\\\\W=3\,\,units`