A ladder is leaning against a building so that the distance from the ground to the top of the ladder is 4 feet less than the length of the ladder. Find the length of the ladder if the distance from the bottom of the ladder to the building is 12 feet.
To find the length of the ladder, we can use the Pythagorean Theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the square of the other two sides.
In this case, we have a right triangle formed by the ladder, the ground, and the building. Let's call the length of the ladder "x". The vertical side of the triangle represents the distance from the ground to the top of the ladder, which is 4 feet less than the length of the ladder. So, we have:
Vertical side = (x - 4) feet
The horizontal side of the triangle represents the distance from the bottom of the ladder to the building, which is given as 12 feet.
Using the Pythagorean Theorem, we can set up the equation:
(Vertical side)^2 + (Horizontal side)^2 = (Length of ladder)^2
Substituting the given values:
(x - 4)^2 + 12^2 = x^2
Now, let's solve for x.
Expanding the equation:
x^2 - 8x + 16 + 144 = x^2
Simplifying:
-8x + 160 = 0
Moving the constant term to the other side:
-8x = -160
Dividing both sides by -8:
x = 20
Therefore, the length of the ladder is 20 feet.
the ladder is the hypotenuse of a right triangle ... 12^2 + (L - 4)^2 = L^2
144 + L^2 - 8 L + 16 = L^2 ... 160 = 8 L