Question 342978: a garden has the shape of a right triangle with one leg 2 meters longer than the other. The hypotenuse is 2 meters less than twice the length of the shorter leg. what is the length of the shorter leg
Answer by destro(1)   (Show Source):
You can put this solution on YOUR website! First draw a right triangle; this will help to identify the formula a^2+b^2=c^2, the pogrom theorem.
Next label the known sides (remember the hypotenuse is c^2 , the longest side).
a^2=〖(x+2)〗^2
b^2=x^2
c^2=〖(2x-2)〗^2
Now transfer the information into an equation 〖(x+2)〗^2+x^2=〖(2x-2)〗^2 .
Now solve for (x) step one “foil” the result is x^2+4x+4+x^2=〖4x〗^2-8x+4
Step two: combine like terms if any,〖2x〗^2+4x+4=〖4x〗^2-8x+4
Step three: Now set the equation = to 0 , 〖4x〗^2-8x+4-〖2x〗^2-4x-4=0(watch you signs) “it’s easy to get mixed up”
Step four : combine terms again; 〖2x〗^2-12x and factor out common factors if any 2x(x-6)
Step six : set the results to =0 2x=0,(x-6)=0, where 2x can = 0, 0is not a valid measurement for the shorter leg Add 6 to both sides of the second result to get x alone 6+x-6=0+6,
X=6 the next two steps are check you answer (plug 6 in for x) if you answer dos not check , look at you math again, and last state the answer in a sentence.
The shorter leg is 6 meters long
|
|
|
