Answer:
Length=15 cm
Width=13 cm
Step-by-step explanation:
-Let x be the width dimension, the length will be (x-2)
-The area of a rectangle is given by the formula;
[tex]A=lw[/tex]
#We substitute the length and width values and equate to the given area:
[tex]A=lw\\195=x\times (x-2)\\\\195=x^2-2x[/tex]
#Rewrite as a quadratic and solve for x:
[tex]195=x^2-2x\\\\x^2-2x-195=0\\\\\# Use \ the \ Quadratic\ formula \ to\ solve:\\\\x_1,x_2=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\\therefore x_1,x_2=\frac{-(-2)\pm\sqrt{(-2)^2-4\times 1\times(-195)}}{2\times 1}\\\\\\x_1=15, x_2=-13[/tex]
Since dimensions are always positve, the x value is 15
x=15
x=13
Hence, the dimensions of the rectangle are length=15 cm and width=13 cm
