   Chapter 3.7, Problem 40E

Chapter
Section
Textbook Problem

# A fence 8 ft tall runs parallel to a tall building at a distance of 4 ft from the building. What is the length of the shortest ladder that will reach from the ground over the fence to the wall of the building?

To determine

To find:

Length of the shortest ladder that will reach from the ground over the fence to the wall of the building.

Explanation

1) Concept:

Use Pythagoras theorem and properties of similar triangles for finding the length of the shortest ladder.

2) Formula:

For a right angle triangle

i) Pythagoras theorem

3) Calculation:

A fence 8 ft tall runs parallel to a tall building at a distance of 4 ft from the building.

To find, Length of the shortest ladder that will reach from the ground over the fence to the wall of the building (L)

DEC~ABC

ABBC=DEEC

Substituting the values from graph,

xy+4=8y

Therefore,

x=8y+4y(1)

ABC is right angle triangle.

By using Pythagoras theorem,

L2=x2+4+y2

Taking square root,

L=x2+4+y2

Substitute x from (1),

L=8y+4y2+4+y2

=64y+42y2+4+y2

=4+y64+y2y2

=4+yy64+y2

Therefore,

L(y)=4y+164+y2

Differentiate with respect to y,

L'y=4y+1ddy64+y2<

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