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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

2. The Pythagorean Theorem and Its Converse

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Exercise 22 Page 635

Compare the square of the largest side length to the sum of the squares of the other two side lengths.

Is a triangle? No.
Explanation: See solution.

Practice makes perfect

We want to determine whether the given side lengths can be the measures of a triangle. To do so, we will use the following theorem.

Triangle Inequality Theorem
The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

Let's check if that is the case.

10+12 ? > 23	23+10 ? > 12	12+23 ? > 10
22 < 23	33 > 12	35 > 10

Therefore, these sides lengths can not form a triangle.

Subchapter links

Exercises p.633-637