Question 325877
ladder is resting against the wall. The top of the ladder touches the wall at a height of 18 ft. Find the length of the ladder if the length is 6ft more tahn its distance from the wall.


The ladder resting against the wall forms its length which is also the hypotenuse of a right triangle. This is what is being asked for.


Let the ladder's distance from the wall be D. Since the length of the ladder is 6 ft more than the ladder's distance from the wall, then the ladder's length is D + 6


We now have 2 legs and the hypotenuse of the right triangle. Based on the pythagorean formula, {{{c^2 = a^2 + b^2}}}, we will have:


{{{(D + 6)^2 = D^2 + 18^2}}}

{{{D^2 + 12D + 36 = D^2 + 324}}}

12D = 288

{{{D = 288/12}}} = 24 ft


This means that the hypotenuse or length of the ladder is {{{highlight_green(30)}}} ft (24 + 6).