SOLUTION: Mellie plans to make a patio 12 feet by 12 feet. She decides to add a border of equal width around the patio to increase the total area to 180 square feet. What is the width of

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Mellie plans to make a patio 12 feet by 12 feet. She decides to add a border of equal width around the patio to increase the total area to 180 square feet. What is the width of       Log On


   

Question 1136797: Mellie plans to make a patio 12 feet by 12 feet. She decides to add a border of equal width around the patio to increase the total area to 180 square feet.
What is the width of this border, to the nearest tenth of a foot?
Answer Choices:
x=0.4
x=0.7
x=6.7
x=7.4
x=12.7

Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
%2812%2B2x%29%2812%2B2x%29=180, x is the uniform width of the border;

2%2A2%286%2Bx%29%5E2=18%2A2%2A5=9%2A2%2A2%2A5
%28x%2B6%29%5E2=45
x%2B6=3%2Asqrt%285%29
x=3%2Asqrt%285%29-6
computeanddecide.
.

Answer by ikleyn(52790) About Me  (Show Source):
You can put this solution on YOUR website!
.
Notice that the old patio is a square.


New patio is a square, too.


The new patio side length is  sqrt%28180%29 = 13.42 feet.


The border width = %2813.42-12%29%2F2 = 0.7 feet (rounded as requested).    ANSWER

Solved.

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To solve this problem, you do not need to setup and to solve a quadratic equation.