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Chapter 2: Q. 2.75 (page 142)

John puts the base of a 13-foot ladder five feet from the wall of his house as shown in the figure. How far up the

wall does the ladder reach?

Short Answer

Expert verified

12 foot far up the wall does the ladder reach

Step by step solution

01

Step 1. Given Information

  • The length of base of right triangle is 5 feet
  • The length of hypotenuse of triangle is 13 feet

We have to find the length of the wall does the ladder reach.

02

Step 2. Name. Choose a variable to represent it.

Let x = the distance of the wall does the ladder reach.

Draw the figure and label it with the given information.

03

Step 3. Translate.

Write the appropriate formula and substitute.

a2+b2=c2x2+52=132

04

Step 4. Solve the equation.x2+25=169

Isolate the variable.

x2=169-25x2=144

Use the definition of square root.

x=144

Simplify.

x=12

05

Step 5. Check

a2+b2=c252+122=13225+144=169169=169verified

12 foot far up the wall does the ladder reach.

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