One of Fermat's other theorems

A Pythagorian Triple (PT) is a list of three numbers $(a,b,c)$ such that $a^2+b^2 = c^2$. Fermat then asked for a PT with the additional property that $a + b$ is also square.

Find a quadruple $(a,b,c,d)$  such that $(a^2+b^2=c^2, a+b=d^2)$
 
( 
Answer:
$a=4565486027761;$
$b=1061652293520;$
$c=4687298610289;$
$d=2372159.$
)