The width of a rectangle is 1 unit less than the length. The area of the rectangle is 72 units. What is the width, in units, of the rectangle?

Question

asked Jan 4, 2021 164k views

1 Answer

Heechul Ryu · Answer 1 · 2021-01-09T16:29:37+0000

Answer:

$Length=9 units\\width=8 units$

Explanation:

Width of the rectangle= W

Length= L

W=(L-1) units

Area= 72 square units

Area of a rectangle= Length*Width

$72=L*(L-1)\\\\72=L^2-L\\\\L^2-L-72=0$

Solving the quadratic equation using the factorization method:

L^2+8L-9L-72=0

Taking common from the equation:

$L(L+8)-9(L+8)=0\\(L+8)(L-9)=0$

$L+8=0\\L=-8$

OR

$L-9=0\\L=9$

The length cannot be negative, therefore: Length= 9 units

$Width=Length-1\\=9-1\\=8 units$

$Length=9 units\\width=8 units$