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Chapter 3: Q17 (page 97)

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

Expert verified

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

Step by step solution

01

. Apply the definition of an equilateral triangle.

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

4n=2n+102n=10

02

鈥� Description of a step.

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

2n2=102n=5

03

Step 3. Description of a step.

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

4n=4脳5=20

04

Step 4. Description of a step.

Substitute 5 for n into2n+10 to find the length of second side.

2n+10=2脳5+10=10+10=20

05

Step 5. Description of a step.

Substitute 5 for n into7n鈭�15 to find the length of third side.

7n鈭�15=7脳5鈭�15=35鈭�15=20

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