Question 1420
So this will form a triangle:
(If you are in high level math, you will notice that it is a 5-12-13 triangle which has sides length of 5, 12 and 13, but if you don't, we will solve it now)
let x be the distance from the ladder to the ground
x^2 + (x-7)^2 = 13^2
x^2 + x^2 - 14x +49 = 169
2x^2 - 14x - 120 = 0
Now use the quardratic formula to solve:
{{{x=(14+-sqrt((-14)^2-4(2)(-120)))/(2(2))}}}
{{{x=(14+-sqrt(1156))/4}}}
{{{x=(14+-34)/4}}}
x = 48/4 or -20/4
x = 12 or -5
Because length of anything can not be a negative number, so 12 is the answer.