SOLUTION: Find the perimeter of a right triangle whose hypotenuse is 2 and whose area is 2. Express your answer in simplest radical form.

Algebra.Com
Question 1103134: Find the perimeter of a right triangle whose hypotenuse is 2 and whose area is 2. Express your answer in simplest radical form.
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39615)   (Show Source): You can put this solution on YOUR website!

Answer by ikleyn(52768)   (Show Source): You can put this solution on YOUR website!
.
The condition describes an IMPOSSIBLE situation,

and below I give the proof to this fact. 

Let the legs be x and y.


Then from the condition you have THESE two equations:

x^2 + y^2 = 2^2

 = 2,


or, EQUIVALENTLY,

x^2 + y^2 = 4,   (1)
xy = 4.          (2)


Then  (x-y)^2 = x^2 -2xy + y^2 = (x^2+y^2) - 2xy = 4 - 2*4 = -4.


But the left side (x-y)^2 is a NON-NEGATIVE value/quantity,  while the right side is NEGATIVE.


Contradiction.

Conclusion: The condition is self-contradictory.


RELATED QUESTIONS

Find the perimeter of a right triangle whose hypotenuse is 2 and whose area is 2. Express (answered by ikleyn)
Find the perimeter of a right triangle whose hypotenuse is 2 and whose area is... (answered by MathLover1,mananth,ikleyn)
The altitude to the hypotenuse of a right triangle divides the hypotenuse into segments... (answered by edjones)
What is the number of square units in the area of a triangle whose sides are 5, 6, and 13 (answered by Timnewman,Alan3354)
Find the lengths of the legs of a right triangle whose hypotenuse is 15^1/2 feet and... (answered by ikleyn)
find the height of a isosceles triangle whose base is 10cm and legs are 20 cm (leave your (answered by KMST)
The perimeter of an isosceles triangle is 80cm. What is the length of the hypotenuse.... (answered by Alan3354)
Using Radical Operations In Real Life Triangle # 1 6 inch (Left)/__\Hypotenuse=x... (answered by friesr)
Find, in simplest radical form, the length of a square whose perimeter is... (answered by Zenock)