equation to find height

Question

A ladder is leaning against a building. The distance from the bottom of the ladder to the building is 8ft less than the length of the ladder. How high up the side of the building is the top of the ladder if that distance is 4ft less than the length of the ladder

Answer 1

Make a little sketch representing the horizontal ground, the vertical side of the building, and the ladder--this will form a right triangle. Now label these sides: hypotenuse (ladder) is x, horizontal leg is x-8, vertical leg is x-4.

 

Plug in these values/expressions into the Pythagorean Theorem. Remember to properly square each binomial (every squared binomial is a trinomial).

 

Collect 'like' terms and simplify the resulting equation. With luck, you'll be able to factor it--if not, use the quadratic formula.

 

I'll bet that this problem is somewhat like some other problems in your textbook, in the current chapter!

 

BEWARE: if the quadratic formula must be used, first calculate the discriminant; if that's negative, there is no solution.