The value of x is: [tex]\frac{4}{3}[/tex]
Recall:
Perimeter of a shape is the sum of all its sides
Thus:
Perimeter of the triangle = [tex]x + x +x+ 4 = 3x + 4[/tex]
Perimeter of the rectangle = [tex]2(2x) + 2(x) = 4x + 2x = 6x[/tex]
We are told that the perimeter of both shapes are equal. Set both perimeters equal and solve for x.
[tex]3x + 4 = 6x[/tex]
Add like terms
[tex]4 = 6x - 3x\\4 = 3x[/tex]
Divide both sides by 3
[tex]\frac{4}{3} = x\\x = \frac{4}{3}[/tex]
The value of [tex]x = \frac{4}{3}[/tex]
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