# A ladder is resting against a wall. The top of the ladder touches the wall at a height of 18 ft. Find the leng

Question:A ladder is resting against a 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 6 ft more than its distance from the wall.

x =distance from wall to ladder x=24 feet
therfore the ladder is 30 feet
x squared + 8squared =(x+6)squared
24 (18)*(6)=24
Do your own homework. Isn't it A squared plus B squared equals C squared? Pythagorean theorum?
Hmmm. Sorry, I can't be bothered to work it out. My calculator is in the other room.
Why don't you get a tape measure and measure the ladder
use the pythagorean theorem:
18=height of wall

x^2+18^2=(x+6)^2
x^2+324=x^2+12x+36
reduce, you get: 288=12x
x=24--the distance ladder is from wall
now, plug it in: x+6
(24)+6=30
using the pythagorean theorem and using x to represent the distance from the wall, the length equals x^2 + 18^2 = (x+6)^2 = x^2 + 18^2 = x^2 + 324 and (x+6)(x+6) = x^2 + 12x + 36, subtract 36 from both sides to get x^2 + 288 = x^2 + 12x, subtract x^2 from both sides to get 288 = 12x, then divide both sides by 12 to get 24 = x, since the length is 6+x the length equals 30
a = ? (base)
b = 18 ft. (height)
c = 6+a (length)

the pythagorean theorem formula is c^2 = a^2 + b^2

so...

(6+a) ^ 2 = a^2 + 18^2

36 + 12a + a^2 = a^2 + 324

36 + 12a + a^2 - a^2 = 324... then a^2 will be cancelled out

36 + 12a = 324

12a = 324 - 36

12a = 288

a = 288 / 12

a = 24 << then this would be the DISTANCE OF THE LADDER FROM THE WALL.

c = 6 + a

c = 6 + 24

c = 30 << then this would be the LENGTH OF THE LADDER.

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to check if it's correct, replace the values on the formula.

c^2 = a^2 + b^2

so, it'll be..

30^ 2 = 24^2 + 18^2

900 = 576 + 324

900 = 900

:)
30 feet
It's simple Pythagorean Theorem. Just plug in the numbers and solve!
32'

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