the top of a 15-foot ladder is 3ft farther up a wall than the foot of the ladder is from the bottom of the wall. how far is the foot of the ladder from the bottom of the wall?
2006-10-17 13:30:50 · 7 answers · asked by michchristine 2 in Science & Mathematics ➔ Mathematics
Let the distance from the foot of the ladder to the bottom of the wall be x.
The ladder resting on the wall forms a triangle with the following sides in feet:
Diagonal = 15
Base = x
Wall Side = (x + 3)
Using Pythagoras theorem,
15^2 = x^2 + (x + 3)^2
Expanding,
225 = x^2 + x^2 + 6x + 9
2x^2 + 6x + 9 - 225 = 0
2x^2 + 6x - 216 = 0
x^2 + 3x - 108 = 0
Factorize,
(x + 12)(x - 9) = 0
We have x = -12 or x = 9
Since distance cannot be a negative number,
we take x = 9
Therefore the foot of the ladder
from the bottom of the wall is 9 feet.
2006-10-17 13:40:51 · answer #1 · answered by ideaquest 7 · 0⤊ 0⤋
Note that the ladder forms a right triangle with the wall and the floor. Let the distance of the foot of the ladder from the bottom of the wall be x - then x+3 is the height of the top of the ladder from the ground, and we have by pythagoras:
x²+(x+3)²=15²
Solving for x:
x²+x²+6x+9=225
2x²+6x=216
x²+3x=108
x²+3x+9/4=441/4
(x+3/2)²=441/4
x+3/2=±21/2
x=-3/2±21/2
Since we are clearly interested only in cases where the distances are positive:
x=-3/2+21/2=9 ft
Edit: screwed up the addition in the last step. It's fixed now.
2006-10-17 20:41:53 · answer #2 · answered by Pascal 7 · 0⤊ 0⤋
Let x be the distance from the bottom of the wall to the foot of the ladder
then x + 3 is the height of the top of the ladder
this is a right triangle with legs of x, x+3 and hypotenuse 15
therefore we use pythagoras
x^2 + (x+3)^2 = 15^2
Expanding,
225 = x^2 + x^2 + 6x + 9
2x^2 + 6x + 9 - 225 = 0
2x^2 + 6x - 216 = 0
x^2 + 3x - 108 = 0
Factorize,
(x + 12)(x - 9) = 0
We have x = -12 or x = 9
Since distance cannot be a negative number,
we take x = 9
solve for x
2006-10-17 20:39:12 · answer #3 · answered by Anonymous · 0⤊ 1⤋
It's a right triangle problem and 15 is your hypotenuse.
You are going to have to use the pythagorean theorem.
Let the distance from the wall at the bottom be x.
Then the other distance is x + 3.
Then you get: X^2 + (X = 3)^2 = 15^2
Can you solve it from there?
2006-10-17 20:42:32 · answer #4 · answered by Alan J 3 · 0⤊ 0⤋
18 foot
2006-10-17 20:41:00 · answer #5 · answered by angel_babii 3 · 0⤊ 0⤋
18 foot
2006-10-17 20:35:22 · answer #6 · answered by Anonymous · 0⤊ 0⤋
ahh **** i hate those math questions crap that play with your brain like that... ok um hold on im thinking.....(squinting eyes)......dude I dont know sorry
2006-10-17 21:02:30 · answer #7 · answered by Caroline M 2 · 0⤊ 0⤋