Question

You are carpeting a room in a house for your job. You have a boss that likes to play jokes, so instead of just giving you the dimensions of the room, he tells you the dimensions in rational expressions. The length of the room is fraction numerator x squared minus x minus 6 over denominator x minus 5 end fractionand the width of the room is fraction numerator x squared minus 6 x plus 5 over denominator x plus 2 end fraction. What is the area of the room in terms of x? How much carpet do you need if x = 10?

Answer 1

Answer:

$x^2-4x+3$

$63\ \text{sq. units}$

Step-by-step explanation:

l = Length = $\dfrac{x^2-x-6}{x-5}$

w = Width = $\dfrac{x^2-6x+5}{x+2}$

Area is given by

$A=lw\\\Rightarrow A=\dfrac{x^2-x-6}{x-5}\times\dfrac{x^2-6x+5}{x+2}\\\Rightarrow A=\dfrac{x^2-3x+2x-6}{x-5}\times\dfrac{x^2-5x-1x+5}{x+2}\\\Rightarrow A=\dfrac{(x-3)(x+2)}{x-5}\times\dfrac{(x-5)(x-1)}{x+2}\\\Rightarrow A=(x-3)(x-1)\\\Rightarrow A=x^2-4x+3$

Area of the room is $x^2-4x+3$.

If $x=10$

Area of the room

$A=x^2-4x+3=10^2-4\times 10+3\\\Rightarrow A=63\ \text{sq. units}$

So, the amount of carpet needed would be $63\ \text{sq. units}$.