A ladder leans stains a wall so the base of the ladder is 5 feet from the wall. If the verticle height reached by the ladder along the wall is x feet and length of the ladder is 1 foot more than the vertical height,find the length of the ladder
A ladder leans stains a wall so the base of the ladder is 5 feet from the wall. If the verticle height reached by the ladder along the wall is x feet and length of the ladder is 1 foot more than the vertical height,find the length of the ladder
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Question
A ladder leans stains a wall so the base of the ladder is 5 feet from the wall. If the verticle height reached by the ladder along the wall is x feet and length of the ladder is 1 foot more than the vertical height,find the length of the ladder.
![**Problem Description:**
A ladder leans against a wall so that the base of the ladder is 5 feet from the wall. If the vertical height reached by the ladder along the wall is x feet and the length of the ladder is 1 foot more than the vertical height, find the length of the ladder.
**Explanation and Steps:**
1. **Identify Known Values:**
- Distance from the wall to the base of the ladder (Adj) = 5 feet.
- Vertical height reached by the ladder (Opp) = x feet.
- Length of the ladder (Hyp) = x + 1 feet.
2. **Apply the Pythagorean Theorem:**
The Pythagorean Theorem states that in a right-angled triangle:
\[
\text{(Hypotenuse)}^2 = \text{(Opposite side)}^2 + \text{(Adjacent side)}^2
\]
Substitute the known values:
\[
(x + 1)^2 = x^2 + 5^2
\]
3. **Simplify the Equation:**
Expand and simplify the equation:
\[
x^2 + 2x + 1 = x^2 + 25
\]
4. **Solve for x:**
Subtract \(x^2\) from both sides of the equation:
\[
2x + 1 = 25
\]
\[
2x = 24
\]
\[
x = 12
\]
5. **Find the Length of the Ladder:**
The length of the ladder = \(x + 1\):
\[
x + 1 = 12 + 1 = 13
\]
**Answer:**
The length of the ladder is 13 feet.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd5dead9f-e821-4d1f-b49e-a22938bc1d4f%2F59f9efff-529f-405f-9109-49e909502d8a%2Flgx117_reoriented.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Description:**
A ladder leans against a wall so that the base of the ladder is 5 feet from the wall. If the vertical height reached by the ladder along the wall is x feet and the length of the ladder is 1 foot more than the vertical height, find the length of the ladder.
**Explanation and Steps:**
1. **Identify Known Values:**
- Distance from the wall to the base of the ladder (Adj) = 5 feet.
- Vertical height reached by the ladder (Opp) = x feet.
- Length of the ladder (Hyp) = x + 1 feet.
2. **Apply the Pythagorean Theorem:**
The Pythagorean Theorem states that in a right-angled triangle:
\[
\text{(Hypotenuse)}^2 = \text{(Opposite side)}^2 + \text{(Adjacent side)}^2
\]
Substitute the known values:
\[
(x + 1)^2 = x^2 + 5^2
\]
3. **Simplify the Equation:**
Expand and simplify the equation:
\[
x^2 + 2x + 1 = x^2 + 25
\]
4. **Solve for x:**
Subtract \(x^2\) from both sides of the equation:
\[
2x + 1 = 25
\]
\[
2x = 24
\]
\[
x = 12
\]
5. **Find the Length of the Ladder:**
The length of the ladder = \(x + 1\):
\[
x + 1 = 12 + 1 = 13
\]
**Answer:**
The length of the ladder is 13 feet.
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