A ladder is 1 foot longer than vertical height in house. The distance of the base of ladder is 7 feet less than vertical height . How far up does the ladder reach?

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Maria -For these types of problems you should ALWAYS sketch a picture of what is going on.  The ladder is leaning against a wall forming a right triangle as follows:The vertical height = aThe hypotenuse (c) = a + 1The bottom leg (b) = a - 7Now simply use the Pythagorean Theorem to get an equation:a^2 + b^ 2= c^2 and substituting in the above:a^2 + (a-7)^2 = (a+1)^2If you simplify the above you will get the following quadratic equation:a^2 -16a +48 = 0Now use factoring:(a-4)(a-12)=0The vertical height (a) can't equal 4 because that would cause the bottom leg to become negative, agree? So, the only correct answer is a = 12.hope this helps