Chapter 3: Q7 (page 110)

Complete.
The lengths of the sides of a triangle are $2 x + 5, 3 x + 10$ and $x + 12$ . Find the values of x that make the triangle isosceles.

Short Answer

Expert verified

The values of x that make the triangle isosceles are 1 and 7.

Step by step solution

Step 1. Description of step.

An isosceles triangle is a triangle in which two of the sides of triangle are equal.

Step 2. Description of step.

Let the two equal sides be $2 x + 5$ and $3 x + 10$ .

Therefore, it can be obtained that:

$2 x + 5 = 3 x + 10 5 - 10 = 3 x - 2 x - 5 = x$

Substitute for x into $2 x + 5$ .

Therefore, it can be obtained that:

$\begin{matrix} 2 (- 5) + 5 = - 10 + 5 \\ = - 5 \end{matrix}$

As $2 x + 5$ is the length of side of triangle and length of side of triangle cannot be negative.

Therefore, $x = - 5$ is not possible.

Step 3. Description of step.

Let the two equal sides be $2 x + 5$ and $x + 12$ .

Therefore, it can be obtained that:

$\begin{matrix} 2 x + 5 = x + 12 \\ 2 x - x = 12 - 5 \\ x = 7 \end{matrix}$

Therefore, the value of x is 7.

Step 4. Description of step.

Let the two equal sides be $3 x + 10$ and $x + 12$ .

Therefore, it can be obtained that:

$\begin{matrix} 3 x + 10 = x + 12 \\ 3 x - x = 12 - 10 \\ 2 x = 2 \\ x = \frac{2}{2} \\ x = 1 \end{matrix}$

Therefore, the value of x is 1.

Step 5. Write the complete statement.

The values of x that make the triangle isosceles are 1 and 7.

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Complete.
The lengths of the sides of a triangle are $2 x + 5, 3 x + 10$ and $x + 12$ . Find the values of x that make the triangle isosceles.

Short Answer

Step by step solution

Step 1. Description of step.

Step 2. Description of step.

Step 3. Description of step.

Step 4. Description of step.

Step 5. Write the complete statement.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Theoretical and Mathematical Physics

Discrete Mathematics

Pure Maths

Applied Mathematics

Logic and Functions

Study anywhere. Anytime. Across all devices.

Complete.The lengths of the sides of a triangle are 2x+5,3x+10and x+12. Find the values of x that make the triangle isosceles.

Short Answer

Step by step solution

Step 1. Description of step.

Step 2. Description of step.

Step 3. Description of step.

Step 4. Description of step.

Step 5. Write the complete statement.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Theoretical and Mathematical Physics

Discrete Mathematics

Pure Maths

Applied Mathematics

Logic and Functions

Study anywhere. Anytime. Across all devices.

Complete.
The lengths of the sides of a triangle are $2 x + 5, 3 x + 10$ and $x + 12$ . Find the values of x that make the triangle isosceles.