Chapter 11: Q52. (page 730)

A ladder is leaning on a building. The base of the ladder is $10 f e e t$ from the building, and the ladder reaches up $15 f e e t$ on the building. How long is the ladder?

Short Answer

Expert verified

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

Step by step solution

Step1. Given

The base of the ladder $= 10 f e e t$

The ladder reaches up to a height of $15 f e e t$

Step2. 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.

Step3. 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,

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

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

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A ladder is leaning on a building. The base of the ladder is $10 f e e t$ from the building, and the ladder reaches up $15 f e e t$ on the building. How long is the ladder?

Short Answer

Step by step solution

Step1. Given

Step2. Draw the rough sketch for the given problem.

Step3. Determine the length of the ladder.

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A ladder is leaning on a building. The base of the ladder is10feetfrom the building, and the ladder reaches up15feeton the building. How long is the ladder?

Short Answer

Step by step solution

Step1. Given

Step2. Draw the rough sketch for the given problem.

Step3. 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

Statistics

Logic and Functions

Theoretical and Mathematical Physics

Geometry

Decision Maths

Study anywhere. Anytime. Across all devices.

A ladder is leaning on a building. The base of the ladder is $10 f e e t$ from the building, and the ladder reaches up $15 f e e t$ on the building. How long is the ladder?