Question

A ladder x 17feet long is leaning against a wall if the wall and the floor form right triangle. Find the height of the wall if the distance between the ladder and the wall is 7feet less then the height of the wall​.

Answer 1

The height of the wall is 24 feet.

Step-by-step explanation:

Let's denote the height of the wall as h. According to the given information, the distance between the ladder and the wall is 7 feet less than the height of the wall, so the distance between the ladder and the wall can be represented as h - 7 feet.

We can use the Pythagorean theorem to relate the height of the wall, the distance between the ladder and the wall, and the length of the ladder. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (in this case, the ladder) is equal to the sum of the squares of the other two sides (in this case, the height of the wall and the distance between the ladder and the wall).

Therefore, we have:

(h - 7)^2 + h^2 = (17^2)

Simplifying this equation:

h^2 - 14h + 49 + h^2 = 289

Combining like terms:

2h^2 - 14h - 240 = 0

Solving this quadratic equation using factoring, completing the square, or the quadratic formula, we find that h = 24 feet or h = -5 feet. Since the height of a wall cannot be negative, the height of the wall is 24 feet.