Chapter 3: Q17 (page 97)

The lengths of sides of a triangle are $4 n, 2 n + 10$ and $7 n - 15$ . Is there a value of n that makes the triangle equilateral? Explain.

Short Answer

Expert verified

The value of n that makes the triangle equilateral is 5.

Step by step solution

. Apply the definition of an equilateral triangle.

An equilateral triangle is a triangle in which all the three sides have the same length.

$\begin{matrix} 4 n = 2 n + 10 \\ 2 n = 10 \end{matrix}$

– Description of a step.

Divide each side of the obtained equation in step 1 by to find the value of n.

$\begin{matrix} \frac{2 n}{2} = \frac{10}{2} \\ n = 5 \end{matrix}$

Step 3. Description of a step.

Substitute 5 for n into 4n to find the length of first side.

$\begin{matrix} 4 n = 4 \times 5 \\ = 20 \end{matrix}$

Step 4. Description of a step.

Substitute 5 for n into $2 n + 10$ to find the length of second side.

$\begin{matrix} 2 n + 10 = 2 \times 5 + 10 \\ = 10 + 10 \\ = 20 \end{matrix}$

Step 5. Description of a step.

Substitute 5 for n into $7 n - 15$ to find the length of third side.

$\begin{matrix} 7 n - 15 = 7 \times 5 - 15 \\ = 35 - 15 \\ = 20 \end{matrix}$

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The lengths of sides of a triangle are $4 n, 2 n + 10$ and $7 n - 15$ . Is there a value of n that makes the triangle equilateral? Explain.

Short Answer

Step by step solution

. Apply the definition of an equilateral triangle.

– Description of a step.

Step 3. Description of a step.

Step 4. Description of a step.

Step 5. Description of a step.

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The lengths of sides of a triangle are 4n,2n+10and 7n-15. Is there a value of n that makes the triangle equilateral? Explain.

Short Answer

Step by step solution

. Apply the definition of an equilateral triangle.

– Description of a step.

Step 3. Description of a step.

Step 4. Description of a step.

Step 5. Description of a step.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Discrete Mathematics

Probability and Statistics

Pure Maths

Statistics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

The lengths of sides of a triangle are $4 n, 2 n + 10$ and $7 n - 15$ . Is there a value of n that makes the triangle equilateral? Explain.