Answer: The required value of x is 20.
Step-by-step explanation: We are given to find the value of x from the figure so that the triangles have the same perimeter.
From the figure, we note that
the lengths of the sides of first triangle are 5, x-4 and x-5.
And, the lengths of the sides of the second triangle are 10, 16 and x-10.
Since both the triangles have the same perimeter, so we get
[tex]5+x-4+x-5=10+16+x-10\\\\\Rightarrow 2x-4=x+16\\\\\Rightarrow 2x-x=16+4\\\\\Rightarrow x=20.[/tex]
Thus, the required value of x is 20.
