SOLUTION: The hypotenus of a right angled triangle is 41mm and the perimeter is 90mm.calculate the lengths of the other two sides.

Algebra ->  Triangles -> SOLUTION: The hypotenus of a right angled triangle is 41mm and the perimeter is 90mm.calculate the lengths of the other two sides.      Log On


   

Question 881184: The hypotenus of a right angled triangle is 41mm and the perimeter is 90mm.calculate the lengths of the other two sides.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
The hypotenuse is the longer side of a right triangle.
The other two sides of a right triangle are called legs.
x= length of one of the legs, in mm.
y= length of the other leg, in mm.

The perimeter is 90mm gives us the equation
x%2By%2B41=90<--->x%2By=90-41<--->x%2By=49<--->y=49-x

The Pythagorean theorem, applied to this particular triangle, tells us that
x%5E2%2By%5E2=41%5E2<--->x%5E2%2By%5E2=1681

system%28y=49-x%2Cx%5E2%2By%5E2=1681%29--->system%28y=49-x%2Cx%5E2%2B%2849-x%29%5E2=1681%29--->system%28y=49-x%2Cx%5E2%2B2401-98x%2Bx%5E2=1681%29--->system%28y=49-x%2C2x%5E2-98x%2B720=0%29--->system%28y=49-x%2Cx%5E2-49x%2B360=0%29
x%5E2-49x%2B360=0--->%28x-40%29%28x-9%29=0--->system%28x=40%2C%22or%22%2Cx=9%29
and those are the lengths (in mm) of the legs of the right triangle, because
system%28y=49-x%2Cx=40%29--->system%28y=9%2Cx=40%29 and system%28y=49-x%2Cx=9%29--->system%28y=40%2Cx=9%29 .
Either way, lengths of the other two sides of the right triangle are
highlight%2840mm%29 and highlight%289mm%29 .