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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

Expert verified

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

Step by step solution

01

Step 1. Description of step.

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

02

Step 2. Description of step.

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

Therefore, it can be obtained that:

2x+5=3x+10510=3x2x5=x

Substitute for x into2x+5 .

Therefore, it can be obtained that:

25+5=10+5=5

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

Therefore, x=5is not possible.

03

Step 3. Description of step.

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

Therefore, it can be obtained that:

2x+5=x+122xx=125x=7

Therefore, the value of x is 7.

04

Step 4. Description of step.

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

Therefore, it can be obtained that:

3x+10=x+123xx=12102x=2x=22x=1

Therefore, the value of x is 1.

05

Step 5. Write the complete statement.

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

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