There is a slide in the park that is 18 feet long. The ladder to the top of the slide is 7.5 feet long. If the ladder and the slide are perpendicular, what is "D", the distance from the top of the slide to the ground? Explain how you got your answer.
To find the distance "D" from the top of the slide to the ground, 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 squares of the other two sides.
In this case, the ladder represents the hypotenuse of the triangle, while the slide represents one of the other two sides. Let's call the unknown side "D".
Using the Pythagorean theorem, we have:
D^2 = (length of the ladder)^2 - (length of the slide)^2
Substituting the given values, we have:
D^2 = 7.5^2 - 18^2
Simplifying further, we get:
D^2 = 56.25 - 324
D^2 = -267.75
Since the result is negative, it means that there is no real solution to this equation. Therefore, there is no distance "D" from the top of the slide to the ground that satisfies the given conditions.
In this case, it seems there may be an error in the problem or the values provided. Please double-check the information given to obtain the correct solution.
the distance from the base of the ladder to the base of the slide is
d = √(7.5^2 + 18^2)
by similar triangles, the desired height h is
h/7.5 = 18/d
figure d, get h.