Question

Complete.

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

Short answer

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 $2x+5$and $3x+10$.

Therefore, it can be obtained that:

$$\begin{gathered} 2x+5=3x+10 \\ 5-10=3x-2x \\ -5=x \end{gathered}$$

Substitute for x into$2x+5$ .

Therefore, it can be obtained that:

$\begin{array}{c}2\left(-5\right)+5=-10+5\\ =-5\end{array}$

As $2x+5$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 $2x+5$and $x+12$.

Therefore, it can be obtained that:

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

Therefore, the value of x is 7.

Step 4. Description of step.

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

Therefore, it can be obtained that:

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

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.