SOLUTION: Find the lengths of the sides of the right triangle. 1/2 x , x+3 , x+2,

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: Find the lengths of the sides of the right triangle. 1/2 x , x+3 , x+2,       Log On


   

Question 1133898: Find the lengths of the sides of the right triangle. 1/2 x , x+3 , x+2,
Found 2 solutions by josgarithmetic, MathLover1:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Pythagorean Theorem Formula! Which side do you believe is the longest?

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
the sides of the right triangle.
%281%2F2%29x ->leg
x%2B3+->hypotenuse
x%2B2->leg

%28x%2B3+%29%5E2=%28%281%2F2%29x%29%5E2%2B%28x%2B2%29%5E2
x%5E2%2B6x%2B9+=x%5E2%2F4%2Bx%5E2%2B4x%2B4...both sides multiply by 4
4x%5E2%2B24x%2B36+=x%5E2%2B4x%5E2%2B16x%2B16
4x%5E2%2B24x%2B36+-x%5E2-4x%5E2-16x-16=0
cross%284x%5E2%29%2B24x%2B36+-x%5E2-cross%284x%5E2%29-16x-16=0
8x%2B20+-x%5E2=0..both sides multiply by -1
x%5E2+-8x+-20+=0.........factor
x%5E2+-10x+%2B2x-20+=0
%28x%5E2+-10x%29+%2B%282x-20%29+=0
x%28x+-10%29+%2B2%28x-10%29+=0
%28x+-+10%29+%28x+%2B+2%29+=+0
solutions:
x=10
x=-2-> disregard negative solution, we need the lengths of the sides


Find the lengths of the sides of the right triangle:
x=10
%281%2F2%2910->highlight%285%29 ->leg
10%2B3+->highlight%2813%29->hypotenuse
10%2B2->highlight%2812%29->leg