SOLUTION: A room has a shape of a right triangle. One of the legs of the triangle is one meter longer than the other. The perimeter of the room is 12 meters. What are the lengths of the t

Algebra ->  Triangles -> SOLUTION: A room has a shape of a right triangle. One of the legs of the triangle is one meter longer than the other. The perimeter of the room is 12 meters. What are the lengths of the t      Log On


   

Question 455886: A room has a shape of a right triangle. One of the legs of the triangle is one meter longer than the other. The perimeter of the room is 12 meters. What are the lengths of the three sides?
Found 2 solutions by richwmiller, Gogonati:
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
a+b+c=12
a=b+1
a^2+b^2=c^2
As I suspected, it is a 3,4, 5 right triangle

Answer by Gogonati(855) About Me  (Show Source):
You can put this solution on YOUR website!
Let's the smaller leg = x m, then the other leg is (x+1) m and the hypotenuse is
sqrt%28x%5E2%2B%28x%2B1%29%5E2%29m.Since the perimeter is 12 m we write the equation:
x%2Bx%2B1%2Bsqrt%28x%5E2%2B%28x%2B1%29%5E2%29=12. We now solve this equation.
sqrt%282x%5E2%2B2x%2B1%29=11-2x, squaring both sides we get:
2x%5E2%2B2x%2B1=121-44x%2B4x%5E2, set the equation to zero:2x%5E2-46x%2B120=0,
divide both sides by 2 we get:x%5E2-23x%2B60=0 solving this equation by
factoring:%28x-3%29%28x-20%29=0. The roots are x=3 and x=20. We reject the solution
x=20 because do not satisfy our problem.
Answer:The lengths are: 3m, 4m, 5m.