SOLUTION: the hypotenuse of a right triangle is 6 cm. One side is 2cm longer than the other. Find the length of the two sides of this right-angle triangle.

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: the hypotenuse of a right triangle is 6 cm. One side is 2cm longer than the other. Find the length of the two sides of this right-angle triangle.       Log On


   

Question 1182033: the hypotenuse of a right triangle is 6 cm. One side is 2cm longer than the other. Find the length of the two sides of this right-angle triangle.
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
the hypotenuse of a right triangle is 6cm. =>c=6
One side is 2cm longer than the other. =>a=b%2B2
Find the length of the two sides of this right-angle triangle
c%5E2=a%5E2%2Bb%5E2......substitute given
6%5E2=%28b%2B2%29%5E2%2Bb%5E2
36=b%5E2%2B4b%2B4%2Bb%5E2
36=2b%5E2%2B4b%2B4...simplify
18=b%5E2%2B2b%2B2
b%5E2%2B2b%2B4-18=0
b%5E2%2B2b-14=0
using quadratic formula you get:
b+=+-1+-+sqrt%2817%29=>disregard negative solution
b+=+-1+%2B+sqrt%2817%29
a=-1+%2B+sqrt%2817%29%2B2=>a=1+%2B+sqrt%2817%29
or approximately:
b=3.12310562561766
a=3.12310562561766%2B2=> a=5.12310562561766


Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
the hypotenuse of a right triangle is 6 cm. One side is 2cm longer than the other.
Find the length of the two sides of this right-angle triangle.
~~~~~~~~~~~~~~~~~~


            This problem has a huge underwater stone.

            I will explain you about it. 


The problem says "one side is 2 m longer than the other side",

but we DON'T KNOW what these two sides are.



They can be two legs of the right angled triangle --- it is the case considered by @MathLover1.



But it may happen, too, that of these two sides, the longer side is the hypotenuse, while the
shorter side is one of the legs.



It is the case MISSED by @MathLover1.



In this case, "one side" is the hypotenuse of the length of 6 cm, and "the other side" is this leg of the length of 6-2 = 4 cm.