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Chapter 1: Q. 4 (page 13)

Use the converse of the Pythagorean Theorem to show that a triangle whose sides are of lengths 11, 60, and 61 is a right triangle.

Short Answer

Expert verified

The given triangle is a right triangle because612=112+602.

Step by step solution

01

Step 1. Given information.

The lengths of a triangle are 11, 60 and 61.

02

Step 2. Show that the triangle is a right triangle.

Converse of the Pythagorean Theorem: In a triangle, if the square of the length of one side equals the sum of the squares of the lengths of the other two sides, the triangle is a right triangle.

The square of the largest side is:

612=3721

The sum of squares of the other two sides is:

602+112=3600+121=3721

03

Step 3. Conclusion.

The given triangle is a right triangle because612=112+602.

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Most popular questions from this chapter

In Problem 17-36, solve each equation algebraically. Verify your solution using a graphing utility.

4y-5=182y

True or False

In using a graphing utility to solve an

equation, exact solutions are always obtained.

A student is asked to find the slope of the line joining (-3, 2) and (1, -4). He states that the slope is 32. Is he correct? If not, what went wrong?

Graph the line containing the point P and having slope m.

P(1,2),m=3

A cereal company finds that the number of people who will buy one of its products in the first month that it is introduced is linearly related to the amount of money it spends on advertising. If it spends \(40,000 on advertising, then 100,000 boxes of cereal will be sold, and if it spends \)60,000, then 200,000 boxes will be sold.

(a) Write a linear equation that relates the amount A spent on advertising to the number x of boxes the company aims to sell.

(b) How much advertising is needed to sell 300,000 boxes of cereal?

(c) Interpret the slope.
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