12. Do the lengths 2.1, 7.2, and 7.5 form a right triangle? Justify your answer.

Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter9: Real Numbers And Right Triangles
Section9.3: The Pythagorean Theorem
Problem 31E
icon
Related questions
icon
Concept explainers
Topic Video
Question
100%
Help
**Question 12: Determining Right Triangles**

**Do the lengths 2.1, 7.2, and 7.5 form a right triangle? Justify your answer.**

To determine if the given lengths can form a right triangle, we can apply the Pythagorean theorem. According to the Pythagorean theorem, for three lengths to form a right triangle, the square of the length of the hypotenuse (the longest side) must equal the sum of the squares of the other two sides. 

Let's denote the given lengths as follows:
- \( a = 2.1 \)
- \( b = 7.2 \)
- \( c = 7.5 \) (hypotenuse, since it is the longest length)

Now, we will check if \( c^2 = a^2 + b^2 \).

Calculate each square:
- \( a^2 = (2.1)^2 = 4.41 \)
- \( b^2 = (7.2)^2 = 51.84 \)
- \( c^2 = (7.5)^2 = 56.25 \)

Then, check the sum of \( a^2 \) and \( b^2 \):
- \( a^2 + b^2 = 4.41 + 51.84 = 56.25 \)

Since \( c^2 = 56.25 \) and \( a^2 + b^2 = 56.25 \), we confirm that the given lengths do satisfy the Pythagorean theorem. Therefore, the lengths 2.1, 7.2, and 7.5 do form a right triangle.
Transcribed Image Text:**Question 12: Determining Right Triangles** **Do the lengths 2.1, 7.2, and 7.5 form a right triangle? Justify your answer.** To determine if the given lengths can form a right triangle, we can apply the Pythagorean theorem. According to the Pythagorean theorem, for three lengths to form a right triangle, the square of the length of the hypotenuse (the longest side) must equal the sum of the squares of the other two sides. Let's denote the given lengths as follows: - \( a = 2.1 \) - \( b = 7.2 \) - \( c = 7.5 \) (hypotenuse, since it is the longest length) Now, we will check if \( c^2 = a^2 + b^2 \). Calculate each square: - \( a^2 = (2.1)^2 = 4.41 \) - \( b^2 = (7.2)^2 = 51.84 \) - \( c^2 = (7.5)^2 = 56.25 \) Then, check the sum of \( a^2 \) and \( b^2 \): - \( a^2 + b^2 = 4.41 + 51.84 = 56.25 \) Since \( c^2 = 56.25 \) and \( a^2 + b^2 = 56.25 \), we confirm that the given lengths do satisfy the Pythagorean theorem. Therefore, the lengths 2.1, 7.2, and 7.5 do form a right triangle.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Knowledge Booster
Application of Algebra
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, trigonometry and related others by exploring similar questions and additional content below.
Similar questions
Recommended textbooks for you
Holt Mcdougal Larson Pre-algebra: Student Edition…
Holt Mcdougal Larson Pre-algebra: Student Edition…
Algebra
ISBN:
9780547587776
Author:
HOLT MCDOUGAL
Publisher:
HOLT MCDOUGAL
PREALGEBRA
PREALGEBRA
Algebra
ISBN:
9781938168994
Author:
OpenStax
Publisher:
OpenStax
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781305652224
Author:
Charles P. McKeague, Mark D. Turner
Publisher:
Cengage Learning
Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,