Explanation Given Information: The length of the sides of a right triangle are consecutive even integers. Formula used: Follow these steps in order to solve the problem. Step 1. Familiarize with the problem or understand the problem. Step 2. Translate the problem into mathematical language or write an equation. Step 3. Carry out the mathematical manipulation to solve the equation. Step 4. Check the answer in the original problem. Step 5. State the answer clearly in a complete sentence. According to the Pythagorean Theorem, for a right triangle, if a and b are the lengths of the legs and c is the length of the hypotenuse, then, a 2 + b 2 = c 2 The principle of zero products is for any real numbers A and B , if A B = 0 then A = 0 or B = 0 . The square of the binomial is the square of the first term, plus twice the product of the two terms, plus the square of the last term, ( A + B ) 2 = A 2 + 2 A B + B 2 , where any real number A is the first term and any real number B is the last term. Calculation: Consider the problem the length of the sides of a right triangle are consecutive even integers. Step 1: Familiarize. Observe the problem carefully. Let x , x + 2 and x + 4 be the length of the sides of the right triangle. Step 2: Translate. According to the Pythagorean Theorem, for a right triangle, if a and b are the lengths of the legs and c is the length of the hypotenuse, then, a 2 + b 2 = c 2 Substitute x for a , x + 2 for b and x + 4 for c in the equation a 2 + b 2 = c 2 . x 2 + ( x + 2 ) 2 = ( x + 4 ) 2 Step 3: Carry out. Solve the equation x 2 + ( x + 2 ) 2 = ( x + 4 ) 2 for x. Use the formula ( A + B ) 2 = A 2 + 2 A B + B 2 ; Substitute x for A and 2 for B in ( A + B ) 2 = A 2 + 2 A B + B 2 and solve ( x + 2 ) 2 and ( x + 4 ) 2 . x 2 + ( x + 2 ) 2 = ( x + 4 ) 2 x 2 + x 2 + 2 ( x ) ( 2 ) + 2 2 = x 2 + 2 ( x ) ( 4 ) + 4 2 x 2 + x 2 + 4 x + 4 = x 2 + 8 x + 16 Combine like terms and solve the equation x 2 + x 2 + 4 x + 4 = x 2 + 8 x + 16 . x 2 + x 2 − x 2 + 4 x − 8 x + 4 − 16 = 0 x 2 − 4 x − 12 = 0 Factor x 2 − 4 x − 12

Elementary Algebra: Concepts and Applications (10th Edition)

10th Edition

ISBN: 9780134441375

Author: Marvin L. Bittinger, David J. Ellenbogen, Barbara L. Johnson

Publisher: PEARSON

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Polygon with three sides, three angles, and three vertices. Based on the properties of each side, the types of triangles are scalene (triangle with three three different lengths and three different angles), isosceles (angle with two equal sides and two equal angles), and equilateral (three equal sides and three angles of 60°). The types of angles are acute (less than 90°); obtuse (greater than 90°); and right (90°).

Chapter 8.6, Problem 61ES

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To calculate: The length of the sides of the right triangle where length of the sides are consecutive even integers.

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Chapter 8.6, Problem 60ES

Chapter 8.6, Problem 62ES

Chapter 8 Solutions

Elementary Algebra: Concepts and Applications (10th Edition)

Ch. 8.1 - Find the square roots of 81.Ch. 8.1 - Prob. 2YT Ch. 8.1 - Prob. 3YT Ch. 8.1 - Prob. 4YT Ch. 8.1 - Prob. 5YT Ch. 8.1 - Prob. 6YT Ch. 8.1 - Prob. 7YT Ch. 8.1 - Prob. 8YT Ch. 8.1 - Prob. 1CYU Ch. 8.1 - Prob. 2CYU

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The length of the sides of the right triangle where length of the sides are consecutive even integers.

Solution Summary: The author explains how to calculate the length of the sides of a right triangle, based on the Pythagorean Theorem.

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To calculate: The length of the sides of the right triangle where length of the sides are consecutive even integers.

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Chapter 8 Solutions