Question

The altitude to the hypotenuse of a right triangle divides the hypotenuse into two segments measuring 11 centimeters and 5 centimeters. to the nearest tenth, what is the length of the shorter leg of the triangle?

Answer 1

a^2 = x^2 - 5^2     where a = altitude, x=shorter leg and y=longer leg.

a^2 = y^2 + 11^2

x^2  - 5^2 = y^2 - 11^2.......... (1)

Also consider the  whole triangle:

x^2 + y^2 = 16^2..........(2)

x^2 - y^2 =   -96  .........(3)                 (from  equation (1))


adding   2 x^2 =   256 + -96 =  160

x^2 = 80 

x = sqrt80

   =  8.94 to nearest hundredth