SOLUTION: Find the exact length of the side of a square whose diagonal is 3 feet. This is what I have. x^2 + x^2 = (x + 3)^2 x^2 + 4x + 9 x^2 - 4x - 9 = 0 x= 4 plus/minus sqrt 39 - 9(1

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Find the exact length of the side of a square whose diagonal is 3 feet. This is what I have. x^2 + x^2 = (x + 3)^2 x^2 + 4x + 9 x^2 - 4x - 9 = 0 x= 4 plus/minus sqrt 39 - 9(1      Log On


   

Question 81780: Find the exact length of the side of a square whose diagonal is 3 feet.
This is what I have.
x^2 + x^2 = (x + 3)^2
x^2 + 4x + 9
x^2 - 4x - 9 = 0
x= 4 plus/minus sqrt 39 - 9(1)(-4)/2(1)
6 + 9 sqrt (2)/2
= 6 + 3 sqrt (2)
Would appreciate any help with this question. Thank you
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Since we know the diagonal is 3 feet we can use Pythagoreans theorem

a%5E2%2Bb%5E2=c%5E2

and replace c with 3 and a%5E2%2Bb%5E2 with x%5E2%2Bx%5E2 like this:

x%5E2%2Bx%5E2=3%5E2

2x%5E2=9 Square 3

2x%5E2=9 Combine like terms

x%5E2=9%2F2 Divide both sides by 2

x=sqrt%289%2F2%29 Take the square root of both sides

Reduce
Since a negative length doesn't make sense our only answer is

x=3%2Fsqrt%282%29

Check:
Plug in the leg 3%2Fsqrt%282%29 into Pythagoreans theorem

%283%2Fsqrt%282%29%29%5E2%2B%283%2Fsqrt%282%29%29%5E2=3%5E2

9%2F2%2B9%2F2=3%5E2 Square each individual term

18%2F2=3%5E2 Add

9=3%5E2 Reduce

sqrt%289%29=sqrt%283%5E2%29 Take the square root of both sides

3=3 works. This verifies our answer.