Question 175284
Let the distance from the bottom of the ladder to the base of the wall be x.
The length of the ladder is 2x-12.
The right triangle formed by the wall at the point where the ladder touches it (12) is the triangle's height.
The base of the triangle is x and the hypotenuse is the ladder of length (2x-12).
Using the Pythagorean theorem:{{{c^2 = a^2+b^2}}} where c = 2x-12, a = 12 and b = x.
{{{(2x-12)^2 = 12^2+x^2}}} Simplify.
{{{4x^2-48x+144 =144+x^2}}} Subtract x^2 from both sides.
{{{3x^2-48x+144 = 144}}} Subtract 144 from both sides.
{{{3x^2-48x = 0}}} Add 48x to both sides.
{{{3x^2 = 48x}}} Divide both sides by 3x.
{{{x = 16}}}
The distance from the bottom of the ladder to the base of the wall is 16 feet.