Question

Suzy Q is getting ready to read decorate her rectangular shape dining room. Her friend is concerned that too little of the floor will be showing after the new rectangular rug is in place. Identify the function that represents the area of the floor not covered by the rug given the following criteria.

The width of the rug is x
The width of the floor is three times the width of the rug.
The length of the rug is two more than the width of the floor.
The length of the floor is twice the length of the rug.

Answer 1

let
x--------> the width of the rug
y--------> the width of the floor
L1------> the length of the rug
L2-----> the length of the floor

we know that
area of the floor not covered by the rug=area of the floor-area of the rug

area of the rug=x*L1
area of the floor=y*L2

y=3x----> equation 1
L1=2+y----> equation 2
L2=2*L1----> equation 3

substitute equation 1 in equation 2
L1=2+3x------> equation 4

substitute equation 4 in equation 3
L2=2*[2+3x]----> equation 5
so
area of the rug=x*L1-----> x*[2+3x]-----> 2x+3x²

area of the floor=y*L2----> 3x*[2*(2+3x)]---> 3x*[4+6x]---> 12x+18x²

area of the floor not covered by the rug=[12x+18x²]-[2x+3x²]
=10x+15x²

the answer is
f(x)=15x²+10x