The sides can be represented by a-d, a, a+d where a+d = the hypotenuse = 15 cm
So the first equation comes from that:
a+d = 15
The second equation comes from the Pythagorean theorem:
(a-d)² + a² = (a+d)²
a² = (a+d)² - (a-d)²
a² = [(a+d)-(a-d)][(a+d)+(a-d)]
a² = [a+d-a+d][a+d+a-d]
a² = [2d][2a]
a² = 4ad
a² - 4ad = 0
a(a - 4d) = 0
a = 0; a - 4d = 0
a = 4d
For a = 0,
not possible because
sides of a triangle are
positive numbers. For a = 4d
a+d = 15
4d+d = 15
5d = 15
d = 3
a = 4(3)
a = 12
The sides are
a-d = 12-3 = 9
a = 12
a+d = 12+3 = 15 (given) 9, 12, 15
Edwin
