A ladder of 25ft is placed against a building in such a way that the distance from the top of the ladder to the ground is 12ft more than the distance from the bottom of the ladder to the building. What is the quadratic equation used to find the distance from the bottom of the ladder to the building?
x^2 + (x+12)^2 = 25^2
To find the quadratic equation used to find the distance from the bottom of the ladder to the building, let's assign variables to the given information.
Let:
- x represent the distance from the bottom of the ladder to the building (in feet).
- (x + 12) represent the distance from the top of the ladder to the ground (in feet).
According to the problem, the ladder has a length of 25ft. Using the Pythagorean theorem, we can create an equation to represent this relationship:
x^2 + (x + 12)^2 = 25^2
Simplifying this equation will give us the quadratic equation we need.