Answer:
17ft wide
Step-by-step explanation:
The room is 9 by 19ft
Length (x) = 19ft
Width(y) = 9ft
Area of the rug = 119ft^2
x*y = 119 ...........(1)
For the second equation we will make sure the strip around the room is uniform in size
9 - x = 19 - y
-x = 19 - 9 -y
-x = 10 - y
x = y - 10 ..........(2)
Put the value x in equation 1
(y - 10)y = 119
y^2 - 10y = 119
y^2 - 10y - 119 = 0
a = 1, b = -10, c= -119
Use quadratic formula to solve the equation
y = (-b +/-√b^2 -4ac) / 2a
y = [-(-10) +/- √ (-10)^2 - 4(1)(-119)] /2(1)
y = (10 +/- √100 + 476) /2
y = (10+/-√ 576 ) / 2
y = (10 +/- 24) / 2
y = (10 + 24) /2 or (10 - 24)/2
y = 34/2 or -14/2
y = 17 or -7
y = 17 ft
Recall that x = y - 10
x = 17 - 10
x = 7ft
