HI is a right triangle; GH = 5, HI = x + 1, GI = x + 9.

Answer 1

GI = longest side = hypotenuse

since x>-1 to keep the sides positive

then x+9>8>5

But there's a problem. You may have a typo or miscopied the problem.

If GI is the hypotenuse, x+1 will be negative.

Odds are you may have meant one side is 15 not 5, then x is about 9, and the sides are about 18, 15 and 10

GI^2 = HI^2 + GH^2

(x+9)^2 = 5^2 + (x+1)^2

x^2 + 18x + 81 = 25 + x^2 + 2x+1

16x = 26-81 = - 55

x =-55/16

x+1 = -39/16

x+9 = 89/16

x+1 is negative

You can try to use either 5 or x+1 as the hypotenuse, but then you get imaginary numbers for x