<PRE><B>Question 191722</B>
use  right  triangle  with  sides  (w)  by  (w+7)  with  hyp  of  13

pythagorous  gives  c^2 = a^2  +  b^2

13^2  =  (w)^2  + (w+7)^2

169  =  w^2  +  w^2  +14w  +49

subtracting  169  both  sides

0  =  2 w^2  +  14w  -120

0=  2  (w^2  +7w  -60)

factoring

0 = 2 ( w+12)  (w-5)

set  (w+12)  = 0,    w=  -12   not  realistic

set  (w-5)  = 0,   w = 5

Dims  are  w=5,  w+7 = 12

check     13^2  =  5^2  +12^2  =  25  +144 = 169    ok</PRE>