Log In Start studying!

Select your language

Suggested languages for you:

Americas

English (US)

Europe

Q47.

Expert-verified

Algebra 1

Found in: Page 659

Book edition Student Edition

Author(s) Carter, Cuevas, Day, Holiday, Luchin

Pages 801 pages

ISBN 9780078884801

Answers without the blur.

Just sign up for free and you're in.

Register for Free I’ll do it later

Short Answer

Determine whether each set of measures can be the lengths of the sides of a right triangle.
10, 12, 15

The given set of measures is not the lengths of the sides of a right triangle.

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given.

The length of the triangle is 10, 12, 15

Step 2. Determine how to identify whether the given measures are the sides of the right triangle, acute triangle, an obtuse triangle.

If c, is the longest side of the triangle, a and b are the other two sides of the triangle then:

(i) If $c^{2} < a^{2} + b^{2}$ , then the triangle is acute.

(ii) If $c^{2} = a^{2} + b^{2}$ , then the triangle is a right triangle.

(iii) If $c^{2} > a^{2} + b^{2}$ , then the triangle is obtuse.

Step 3. Determine whether the given set of measures can be the lengths of the sides of a right triangle.

The triangle is having sides of measures 10, 12, and 15.

The longest side of the triangle is 15.

Therefore, the value c is 15.

Therefore, the values of a and b are 10 and 12 respectively.

Now, it can be obtained that:

$\begin{matrix} a^{2} = 10^{2} = 100 \\ b^{2} = 12^{2} = 144 \\ c^{2} = 15^{2} = 225 \\ a^{2} + b^{2} = 100 + 144 = 244 \end{matrix}$

It can be noticed that:

$\begin{matrix} a^{2} + b^{2} = 244 \\ a^{2} + b^{2} \neq c^{2} \end{matrix}$

As, $c^{2} \neq a^{2} + b^{2}$ , therefore, the triangle is not a right triangle.

Therefore, the given set of measures is not the lengths of the sides of a right triangle.

Most popular questions for Math Textbooks

Graph the function, and compare to the parent graph. State the domain and range.

$y = 3 \sqrt{x}$

Determine whether each set of measures can be the lengths of the sides of a right triangle.

12, 16, 21

Graph the function, and compare to the parent graph. State the domain and range.

$h (x) = \sqrt{x + 3}$

How many times does the graph of $y = x^{2} - 4 x + 10$ cross the $x$ -axis?

Solve the equation.

$x^{2} - 7 x + 10 = 0$

Want to see more solutions like these?

Sign up for free to discover our expert answers

Get Started - It’s free

Recommended explanations on Math Textbooks

94% of StudySmarter users get better grades.

Sign up for free