Camilla needs to fix the window on the front of her house the bottom of the window is 16 ft from the ground she only has a 20 ft ladder how far from the base of the house should he set up the letter so that the top of the letter is exactly at the bottom of the window
To solve this problem, we can use the Pythagorean theorem. Let's denote the distance from the base of the ladder to the base of the house as 'x' and the height of the ladder as 'h'.
According to the problem, Camilla has a 20 ft ladder, so h = 20 ft.
We also know that the bottom of the window is 16 ft from the ground. Since the top of the ladder should reach the bottom of the window, the total height covered by the ladder is h + 16 ft.
Using the Pythagorean theorem, we can write the equation: x^2 + (h + 16)^2 = h^2.
Expanding this equation, we get:
x^2 + h^2 + 32h + 256 = h^2.
Simplifying the equation, we have:
x^2 + 32h + 256 = 0.
Since the value of 'h' is known (h = 20 ft), we can substitute it into the equation:
x^2 + 32(20) + 256 = 0.
Solving this equation, we get:
x^2 + 640 + 256 = 0.
x^2 + 896 = 0.
Subtracting 896 from both sides, we have:
x^2 = -896.
Since we cannot have a negative distance, it is not possible to set up the ladder so that the top is exactly at the bottom of the window with a 20 ft ladder. Camilla might need to get a taller ladder or use alternative methods to fix the window.