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

Answer:

$Length=9\,\,units$

Step-by-step 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= $Length\times Width$

$27=Length\times Width$

$27=L\times (L-6)$

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

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

Equating to zero:

$L+3=0\\L=-3$

OR, Similarly:

$L=9$ units

The length of the rectangle cannot be negative,

therefore,

  $Length=9\,\,units$

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