SOLUTION: The hypotenuse of a right triangle is 4cm less than twice as long as one of the other side. If the third side is 16 cm long, find the length of the hypotenuse.

Algebra ->  Pythagorean-theorem -> SOLUTION: The hypotenuse of a right triangle is 4cm less than twice as long as one of the other side. If the third side is 16 cm long, find the length of the hypotenuse.      Log On


   

Question 636003: The hypotenuse of a right triangle is 4cm less than twice as long as one of the other side. If the third side is 16 cm long, find the length of the hypotenuse.
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

The hypotenuse of a right trianglehighlight%28y%29 is 4cm less than twice as long as one of the other side highlight%28x%29

If the third side is 16 cm long, find the length of the hypotenuse.

Applying the Pythagorean Theorem

 16^2 + x^2 = y^2      | y+=+%282x-4%29

 256 + x^2 = 4x^2 - 16x + 16 

  3x^2 -16x - 240 = 0

x+=+%2816+%2B-+sqrt%283136%29%29%2F%286%29+ 

x+=+%2816+%2B-+56%29%2F%286%29+ 

        x = 12cm, the other leg    (throwing out negative solution for unit measure)

 Hypotenuse is 20cm        2%2A12+-+4

and...

 +16%5E2+%2B+12%5E2+=+20%5E2