# SOLUTION: I need help solving this problem. this is the work i did so far: there is a triangle on one side there is (x-2) the other side is (x-4) and the longest side is 10. (x-2)^2+

Algebra ->  -> SOLUTION: I need help solving this problem. this is the work i did so far: there is a triangle on one side there is (x-2) the other side is (x-4) and the longest side is 10. (x-2)^2+       Log On

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 Click here to see ALL problems on Pythagorean-theorem Question 92081: I need help solving this problem. this is the work i did so far: there is a triangle on one side there is (x-2) the other side is (x-4) and the longest side is 10. (x-2)^2+ (x-4)^2= 10^2 (x-2)(x-2)+ (x-4)(x-4)= 100 x^2 + -2x + -2x + 4 + x^2 + -4x + -4x + 16 2x^2 + -12x + 20 = 100 Answer by jim_thompson5910(29613)   (Show Source): You can put this solution on YOUR website!I'll pick up where you left off (your steps are correct) Subtract 100 from both sides Combine like terms Now let's use the quadratic formula to solve for x: Starting with the general quadratic the general solution using the quadratic equation is: So lets solve ( notice , , and ) Plug in a=2, b=-12, and c=-80 Negate -12 to get 12 Square -12 to get 144 (note: remember when you square -12, you must square the negative as well. This is because .) Multiply to get Combine like terms in the radicand (everything under the square root) Simplify the square root (note: If you need help with simplifying the square root, check out this solver) Multiply 2 and 2 to get 4 So now the expression breaks down into two parts or Lets look at the first part: Add the terms in the numerator Divide So one answer is Now lets look at the second part: Subtract the terms in the numerator Divide So another answer is So our possible solutions are: or Now lets find each of the leg's lengths: Leg A: Plug in x=10 Plug in x=-4 Since a negative length doesn't make sense, the solution x=-4 must be discarded Leg B: Plug in x=10 Plug in x=-4 Since a negative length doesn't make sense, the solution x=-4 must be discarded So the only solution is where the lengths of the legs are 8 and 6 (or 6 and 8)