Catarina and Tom want to buy a rug for a room that is 9 by 19 feet. They want to leave an even strip of flooring uncovered around the edges of the room. How wide a strip will they have if they buy a rug with an area of 119 square feet?

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