Question 31464
If you picture a ladder leaning against the wall, you can see that it forms a right triangle such that the ladder is the hypotenuse.

Let x = the length of the ladder (in ft).

We know that one side of the triangle is 4ft, and the other side of the triangle is 1/5 the length of the ladder, which is (1/5)x.

So, if we plug this knowledge into the pythagorean theorem, we have:

a = 4ft
b = x/5
c = x

{{{(4)^2 + (x/5)^2 = x^2}}}


{{{16 + x^2/25 = x^2}}}


{{{16 = x^2 - x^2/25}}}


{{{16 = (24/25)x^2}}}


{{{16*(25/24)= x^2}}}


{{{2*(25/3)= x^2}}}


{{{50/3 = x^2}}}


{{{sqrt(50/3) = x}}}


{{{5*sqrt(2/3) = x}}}


So, the length of the ladder is {{{5sqrt(2/3)}}} ft, or approx 5.816 ft.