SOLUTION: the length of a side of a triangle are x cm,(x+1)cm and (x+2)cm.Determine x so that this triangle is a right angled triangle

Algebra ->  Triangles -> SOLUTION: the length of a side of a triangle are x cm,(x+1)cm and (x+2)cm.Determine x so that this triangle is a right angled triangle      Log On


   

Question 662313: the length of a side of a triangle are x cm,(x+1)cm and (x+2)cm.Determine x so that this triangle is a right angled triangle
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

x+cm,
%28x%2B1%29cm and
%28x%2B2%29cm.........this is hypotenuse

%28%28x%2B2%29cm%29%5E2=+x%5E2%2B%28%28x%2B1%29cm%29%5E2
%28%28x%2B2%29cm%29%5E2=+x%5E2%2B%28x%5E2%2B2x%2B1%29cm%5E2
%28%28x%2B2%29cm%29%5E2=+%282x%5E2%2B2x%2B1%29cm%5E2
%28x%5E2%2B4x%2B4%29cross%28cm%5E2%29=+%282x%5E2%2B2x%2B1%29cross%28cm%5E2%29
x%5E2%2B4x%2B4=+2x%5E2%2B2x%2B1
0=+2x%5E2-x%5E2-4x-4%2B2x%2B1
0=+x%5E2-2x-3
x%5E2-2x-3=0...replace -2x with -3x%2Bx
x%5E2-3x%2Bx-3=0...group
%28x%5E2-3x%29%2B%28x-3%29=0
x%28x-3%29%2B%28x-3%29=0
%28x%2B1%29%28x-3%29=0
solutions:
if x%2B1=0...=>...x=-1...we can't take negative value for a sside of a triangle
if x-3=0...=>...x=3...this is our solution:

so, the sides are
x=3+cm,
%28x%2B1%29=4cm and
%28x%2B2%29=5cm