Rectangle dimensions

[tiny7smom]

The length of a rectangle is 19 inches less than the perimeter. The area is 1,400 square inches. What are the dimensions?

 

[soroban]

Hello, tiny7smom!

There must be typo.
Please check the numbers in the problem.

The length of a rectangle is 19 inches less than the perimeter.
The area is 1,400 square inches.
What are the dimensions?

"Length is Perimeter minus 19."
. . \(\displaystyle L \;=\; (2L + 2W) - 19 \quad\Rightarrow\quad L\:=\:19 - 2W\) .[1]

"Area is 1400."
. . \(\displaystyle LW \:=\:1400\) .[2]

Substitute [1] into [2]: .\(\displaystyle (19-2W)W \:=\:1400 \quad\Rightarrow\quad 2W^2 - 19W + 1400 \:=\:0 \)

And this quadratic equation has no real roots.