the medians of the two legs of a right triangle are 6 radical 2 and 3 radical 17. find the hypotenuse of the right triangle

Question

The medians of the two legs of a right triangle are 6√2 and 3√17. Find the hypotenuse of the right triangle

Answer 1

Draw a right triangle

 

length of base =2b; length of other side be 2h

 

3^2*17 = h^2 + (2b)^2

 

153 = h^2 + 4b^2

 

6^2*2 =(2h)^2 + b^2

 

72 = 4h^2 + b^2

 

solving both equations simultaneously; gives h = 3 and b = 6

 

(Hypothenuse)^2 = (2b)^2 + (2h)^2 = 12^2 + 6^2 

 

hypothenuse = 180^1/2 = 6*5^1/2 = 13.4