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Algebra 1

Carter, Cuevas, Day, Holiday, Luchin

$Math Studyset 91影视 Explanations$ Math

Student Edition 路 801 pages

ISBN: 9780078884801

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

01

Step1. Given

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

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

02

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.

03

Step3. Determine the length of the ladder.

In the triangle $B C D$ , $鈭� B C D$ 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,

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

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

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