Answer: The required value of x is 10 and the perimeter is 28.
Step-by-step explanation: Given that the square and the triangle have equal perimeters.
We are to find the value of x and the perimeter.
From the given figure, we note that
length of a side of the square, a = x-3
and the lengths of the sides of the triangle are x, x and 8.
According to the given information, we get
[tex]4a=x+x+8\\\\\Rightarrow 4(x-3)=2x+8\\\\\Rightarrow 4x-12=2x+8\\\\\Rightarrow 4x-2x=8+12\\\\\Rightarrow 2x=20\\\\\Rightarrow x=\dfrac{20}{2}\\\\\Rightarrow x=10.[/tex]
Also, the perimeter of the square and the triangle is
[tex]4(x-3)=4(10-3)=4\times7=28[/tex]
Thus, the required value of x is 10 and the perimeter is 28.
