Question

Complete.

7. 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 isoscelesare1 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 –5 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 the side of the triangle and length of the side of the 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:

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

Therefore, the value of x is 1.

Step 5. Write the complete statement.

The values of x that make the triangle isoscelesare1 and 7.