SOLUTION: a right angled triangle has a hypotenuse that is 2 cm longer than one of its sides and 9 cm longer than the other side. state the length of sides of the triangle. this is my wor

Question 994112: a right angled triangle has a hypotenuse that is 2 cm longer than one of its sides and 9 cm longer than the other side. state the length of sides of the triangle.
this is my working
let c=hypotenuse , b=one of its sides,c=other of its sides
a=c-2
b=c-9
c^2=(c-2)^2+(c-9)^2
c^2=c^2-4c+4+c^2-18c+81
0=c^2-22c+85
0=(c-17)(c-5)
when c=17, a=15
when c=5, a=3
when c=17, b=8
when c=5, b=-4
so, what is the actual length of the sides of the triangle, it doesnt make sense if the length has a negative value. pls help me :)
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

17, 15, and 8 are the measures of the sides. A negative value for a measure of length is absurd, hence

is what is called an extraneous root. This is a frequent occurrence when you have to square your variable in order to solve the problem as you did in this case. This is the reason they have been telling you since the 4th grade to check your work; to make sure your answer really is a solution to the problem.

John

My calculator said it, I believe it, that settles it

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