Question 165009
Draw a picture of the problem -- label everything you know -- this helps!
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Let x = length of the ladder
x-3 = distance  from the bottom of the ladder to the wall
x-4 = distance of its top to the ground
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Since the wall the the ground forms a right angle, this is a "right triangle".  We can apply Pythagorean theorem:
(x-3)^2 + (x-4)^2 = x^2
x^2-6x+9 + x^2-8x+16 = x^2
2x^2-14x+25 = x^2
x^2-14x+25 = 0
Since we can't factor, we must resort to the quadratic formula.  Doing so, will result in:
x = {11.90, 2.10}
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We can toss out the 2.10 answer leaving us with:
11.90 feet (length of the ladder)
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Details of quadratic:
*[invoke quadratic "x", 1, -14, 25 ]