SOLUTION: A rectangular patio is 7 feet longer than it is wide. Determine the dimensions of the patio if it measures 13 feet diagonally.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: A rectangular patio is 7 feet longer than it is wide. Determine the dimensions of the patio if it measures 13 feet diagonally.      Log On


   

Question 178294: A rectangular patio is 7 feet longer than it is wide. Determine the dimensions of the patio if it measures 13 feet diagonally.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Length: x%2B7 and Width: x

a%5E2%2Bb%5E2=c%5E2 Start with Pythagorean's Theorem

%28x%2B7%29%5E2%2B%28x%29%5E2=13%5E2 Plug in a=x%2B7, b=x, and c=13

%28x%2B7%29%5E2%2B%28x%29%5E2=169 Square 13 to get 169

x%5E2%2B14x%2B49%2Bx%5E2=169 FOIL

x%5E2%2B14x%2B49%2Bx%5E2-169=0 Subtract 169 from both sides.

2x%5E2%2B14x-120=0 Combine like terms.

2%28x%2B12%29%28x-5%29=0 Factor

x%2B12=0 or x-5=0 Set each factor equal to zero

x=-12 (we'll ignore this one) or x=5 Solve for "x"

So the width of the patio is 5 ft. This makes the length 12 ft (add 7 to the width)