T tiny7smom New member Joined Aug 31, 2012 Messages 8 Aug 31, 2012 #1 The length of a rectangle is 19 inches less than the perimeter. The area is 1,400 square inches. What are the dimensions?
The length of a rectangle is 19 inches less than the perimeter. The area is 1,400 square inches. What are the dimensions?
S soroban Elite Member Joined Jan 28, 2005 Messages 5,584 Sep 1, 2012 #2 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? Click to expand... "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.
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? Click to expand... "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.
