Question

The length of a rectangle is 2 centimeters less than its width. What are the dimensions of the rectangle if its area is 195 square centimeters?

Answer 1

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;

$A=lw$

#We substitute the length and width values and equate to the given area:

$A=lw\\195=x\times (x-2)\\\\195=x^2-2x$

#Rewrite as a quadratic and solve for x:

$195=x^2-2x\\\\x^2-2x-195=0\\\\\# Use \ the \ Quadratic\ formula \ to\ solve:\\\\x_1,x_2=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\\therefore x_1,x_2=\frac{-(-2)\pm\sqrt{(-2)^2-4\times 1\times(-195)}}{2\times 1}\\\\\\x_1=15, x_2=-13$

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