Question 191550
assume  problem  is  right  triangle  with  sides  (l-8),  (l-4),  and  hypotenuse  of  l

pythagorous  theorem  states  c^2 = a^2 + b^2

l^2 = (l-8)^2  +  (l-4)^2

l^2 = (  l^2 -16 * l +64)  +  (l^2  -8*l +16)

L^2 =  2*l^2  -  24*l  + 80

0  =    l^2  -24*l  + 80

factoring  0  =  ( l -20)   (  L-4)

l-20  = 0.   l=+20

l-4  =  0,   l=4      but  l-8  and  l-4  are  positive  lengths  therefore  l  cannot   equal 4  

sides  of  triangle  are    20,   l-8  =  12,  and  l-4  =16    (  height   up  bldg)