A ladder is resting against a wall. The top of the ladder touches the wall at a height of 15 ft. Find the length of the ladder if the length is 5 ft more than its distance from the wall.Group of answer choices
Question
A ladder is resting against a wall. The top of the ladder touches the wall at a height of 15 ft. Find the length of the ladder if the length is 5 ft more than its distance from the wall.Group of answer choices
Solution
This problem can be solved using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Let's denote:
- the length of the ladder (the hypotenuse in our case) as L,
- the distance from the wall (one of the other two sides) as D.
From the problem, we know that:
- The ladder touches the wall at a height of 15 ft (this is the length of the other side of the triangle).
- The length of the ladder is 5 ft more than its distance from the wall, so we can write this as L = D + 5.
We can now use the Pythagorean theorem to write an equation and solve for D:
(D)^2 + (15)^2 = (L)^2 Substitute L with D + 5: (D)^2 + (15)^2 = (D + 5)^2
Solve this equation to find the value of D, and then substitute D into the equation L = D + 5 to find the length of the ladder.
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