SOLUTION: 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. Find the sum, in cm, of the lengths of t

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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. Find the sum, in cm, of the lengths of the this sides of all triangles that satisfy this criteria.
A) 63
B) 56
C) 28
D) 72
E) 65
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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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%282401-98a%29
using the graphing feature on a Ti83. x=a; y=b
enter
y = sqrt%282401-98x%29
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