julia needs to purchase a ladder that just reaches the top of a 16 foot building. if the bottom of the ladder will be placed 12 feet from the base of the building how long should julia's ladder be?
20 feet. Consider the Pythagorean theorem and right triangles with 3:4:5 side length ratios
you do a2(squared) plus b2(squared) equals c2(squared)
a squared plus b squared equals c squared.
To find out how long Julia's ladder should be, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side, which is the ladder in this case) is equal to the sum of the squares of the other two sides.
In this scenario, the ladder (hypotenuse) forms a right-angled triangle with the building. Let's call the length of the ladder 'L', the height of the building 'H', and the distance from the base of the building to the ladder 'D'. According to the given information, H = 16 feet, and D = 12 feet.
Applying the Pythagorean theorem, we have:
L^2 = H^2 + D^2
Substituting the given values:
L^2 = 16^2 + 12^2
L^2 = 256 + 144
L^2 = 400
To solve for L, we take the square root of both sides:
L = √400
L = 20
Therefore, Julia's ladder should be 20 feet long in order for it to just reach the top of the 16-foot building when placed 12 feet away from the base.