Answer:
The shortest side = 5
Step-by-step explanation:
Call one side = a
The middle side = b
the hypotenuse = c
a^2 + b^2 = c^2
a^2 + b^2 = 13^2
a^2 + b^2 = 169
a + b + c = 30
a + b + 13 = 30
a + b = 17
b = 17 - a
a^2 + b^2 = 169
a^2 + (17 - a)^2 = 169
a^2 + (289 - 34a + a^2) = 169
a^2 + a^2 - 34a + 289 = 169 Subtract 169 from both sides
2a^2 - 34a + 289 - 169 = 0
2a^2 - 34a + 120 = 0 Divide by 2
a^2 - 17a + 60 = 0
This quadratic is easily factored. You need two numbers that add to - 17 and multiply to 60
(a - 5) * (a - 12) = 0 Both give you positive answers. You only want the shortest side
a - 5 = 0
a = 5 Is 5 the shortest side?
a - 12 = 0
a = 12 Yes 5 is the shortest side.
