Question 903536
The sides of certain right triangles are Pythagorean triples, the sum of one of the sides of the triangle plus the hypotenuse equals 49 cm.
a + c = 49
c = (49-a)
Phythag: a^2 + b^2 = c^2
replace c 
a^2 + b^2 = (49-a)^2
a2 + b^2 = 2401 - 98a + a^2
subtract a^2 from both sides
b^2 = 2401 - 98a
b = {{{sqrt(2401-98a)}}}
using the graphing feature on a Ti83. x=a; y=b
enter
y = {{{sqrt(2401-98x)}}}
using the table found only 3 integer solutions
x=12; y=35
x=20; y=21
x=24; y=7
Corresponds to triples of (subtract x from 49 to find c
a=12; b=35; c=37; sum: 84
a=20; b=21; c=29; sum: 70
a=24; b=7;  c=25; sum: 56