Chapter 10: Q52. (page 659)

A ladder is leaning on a building. The base of the ladder is 10 feetfrom the building, and the ladder reaches up 15 feeton the building. How long is the ladder?

Short Answer

Expert verified

The ladder is $5 \sqrt{13}$ feet long

Step by step solution

Step 1. Given.

The base of the ladder $= 10 feet$

The ladder reaches up to a height of 15 feet

Step 2. Draw the rough sketch for the given problem.

The rough sketch for the given problem is:

$A C$ is the building and $C E$ is the ground.

$B C$ is the height up to which ladder can reach on the building.

$C D$ is the distance of the base of the ladder from the building.

$B D$ is the ladder.

Step 3. Determine the length of the ladder.

In the triangle $B C D$ , $∠ B C D$ is a right angle. Therefore, the triangle $B C D$ is right-angled.

According to the Pythagorean theorem, it can be noticed that:

${(B D)}^{2} = {(B C)}^{2} + {(C D)}^{2}$

Therefore,

${(B D)}^{2} = {(B C)}^{2} + {(C D)}^{2} {(B D)}^{2} = {(15)}^{2} + {(10)}^{2} {(B D)}^{2} = 225 + 100 {(B D)}^{2} = 325 B D = \sqrt{325} B D = \sqrt{25 \times 13} B D = \sqrt{5^{2} \times 13} B D = 5 \sqrt{13}$

Therefore, the ladder is $5 \sqrt{13}$ feet long.

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

A ladder is leaning on a building. The base of the ladder is 10 feetfrom the building, and the ladder reaches up 15 feeton the building. How long is the ladder?

Short Answer

Step by step solution

Step 1. Given.

Step 2. Draw the rough sketch for the given problem.

Step 3. Determine the length of the ladder.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Applied Mathematics

Probability and Statistics

Theoretical and Mathematical Physics

Calculus

Mechanics Maths

Study anywhere. Anytime. Across all devices.