Question

The top of a 15-foot ladder is 3 feet farther up a wall than the foot of the ladder is from the bottom of the wall. How far up is the foot of the ladder from the bottom of the wall?


The answer is 9 but I don’t know how to get there.

Answer 1

Check the picture below.

$\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2 \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases}\implies 15^2=x^2+(x+3)^2 \\\\\\ 225=x^2+(x^2+6x+9)\implies \implies 225=2x^2+6x+9 \\\\\\ 0=2x^2+6x-216\implies 0=2(x^2+3x-108) \\\\\\ 0= x^2+3x-108\implies 0=(x-9)(x+12)\implies x= \begin{cases} 9 ~~ \checkmark\\\\ -12 \end{cases}$

let's notice that "x" does have two valid values, however for this scenario 'x" cannot be negative, so we don't use that one.