Question

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?

Answer 1

17ft wide

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