91Ó°ÊÓ

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

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.

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.

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.

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