a) Since we know they have equal perimeters, we can set them equal to each other. First, let's recap the perimeters of squares and triangles (s = side):
[tex]P_s = 4s/tex]
[tex]P_t = 3s=s+s+s[/tex]
Now, we can set up our equation:
[tex]4(x-3) = 8 + x + x[/tex]
[tex]4x-12 = 8+2x[/tex]
We can solve for x:
[tex]2x-12=8[/tex]
[tex]2x = 20[/tex]
[tex]x = \frac{20}{2} = 10[/tex]
So, x = 10.
b) We known the perimeter formulas and we have what x is. So, let's just plug and chug.
Square:
[tex]4(x-3) = 4(10-3) = 40-12 = 28[/tex]
So, the perimeter of the square is 28 units².
Since their perimeters are equal the perimeter of the triangle is also 28 units²
