SOLUTION: the hypotenuse of a right triangle exceeds the length of one leg by 1 and is 3less than 4 times the length of the other leg. determine the length of each leg of the right triangle

Algebra ->  Triangles -> SOLUTION: the hypotenuse of a right triangle exceeds the length of one leg by 1 and is 3less than 4 times the length of the other leg. determine the length of each leg of the right triangle       Log On


   

Question 637005: the hypotenuse of a right triangle exceeds the length of one leg by 1 and is 3less than 4 times the length of the other leg. determine the length of each leg of the right triangle
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

the hypotenuse of a right triangle exceeds the length of one leghighlight%28x%29 by 1 and is 3less than 4 times the length of the other leghighlight%28y%29. 

Question states*** hypotenuse can be expressed in two ways...

 x + 1 = 4y-3    Or    x+=+4y-4

Using the Pythagorean Theorem

  x^2 + y^2 = (4y-3)^2

%284y-4%29%5E2 + y^2 = (4y-3)^2

 y^2 -8y +7 = 0

(y-7)(y-1) = 0,

  y = 7, x = 24 and hypotenuse is  25    x%2B1