Answer:
The side lengths of the triangle, in order, are 11 inches, 60 inches, 61 inches.
Step-by-step explanation:
Let the shorter leg be x, the longer leg, y and the hypotenus, z.
y = 16 + 4x
z = 17 + 4x
By Pythagoras rule,
z^2 = x^2 + y^2
(17+4x)^2 = x^2 + (16+4x)^2
that is,
x^2 - 8x - 33 = 0 (A quadratic equation)
By factorising,
(x+3)(x-11)=0
either x = -3 or x = 11.
But length cannot be negative. Hence, -3 is dicarded.
x = 11 inches
y = 16 + 4x = 60 inches
z = 17 + 4x = 61 inches
