SOLUTION: A ladder is two feet longer than the height of a certain wall. When the top of the ladder is placed against the top of the wall, the distance from the base of the ladder to the bo

Question 375986: A ladder is two feet longer than the height of a certain wall. When the top of the ladder is placed against the top of the wall, the distance from the base of the ladder to the bottom of the wall is equal to the height of the wall. How high is the wall?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A ladder is two feet longer than the height of a certain wall.
When the top of the ladder is placed against the top of the wall, the distance
from the base of the ladder to the bottom of the wall is equal to the height of the wall.
How high is the wall?
:
This is a right triangle problem, a^2 + b^2 = c^2
The distance from the base to the wall, and the height of the wall are given
as equal: a = b, the ladder is the hypotenuse, c = a+2
:
We can write the equation:
a^2 + a^2 = (a+2)^2
:
2a^2 = a^2 + 4a + 4
Combine on the left
2a^2 - a^2 - 4a - 4 = 0
a^2 - 4a - 4 = 0
Solve this using the quadratic formula
Positive solution; a = 4.828 ft height of the wall
:
6.828 ft = length of ladder
Seems kind of short, check solution by finding the ladder length
Ladder = enter into a calc
Ladder = 6.828; confirms our solution
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