Right-angled 81019

In the right-angled triangle ABC (AB is the hypotenuse), a : b = 24 : 7, and the height to the side c = 12.6 cm applies. Calculate the lengths of the sides of triangle ABC.

Correct answer:

a =  45 cm
b =  13.125 cm
c =  46.875 cm

Step-by-step explanation:

 a : b = 24 : 7  = 24x : 7x h=12.6 cm  c2 = a2 + b2 = (24x)2 + (7x)2 c = x   242 + 72 c = x   25 = 25x  S = 2a b = 2c h  a b = c h 24x 7 x = 25 x h 24x 7 = 25 h  x=24 725 h=24 725 12.6=815=1.875 cm  a=24 x=24 1.875=45 cm
b=7 x=7 1.875=8105 cm=13.125 cm
c=25 x=25 1.875=8375=46.875=8375 cm=46.875 cm   Verifying Solution:  r=a/b=45/13.125=7243.4286 c2=a2+b2=452+13.1252=8375=46.875 cm



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