What we are required to do here - is to find the perimeter of the rectangle, and the perimeter of the square. Then find what value makes them equal.
Perimeter of a Square is four-times the length of one of its sides. P = 4l
From the image, the length of one side of the square is 3x
So, the perimeter of the square is now:
Four-times 3x
Perimeter of the square = 4(3x) = 12x
Now, we need to find the perimeter of the given rectangle.
The Perimeter of a Rectangle is given as: 2l + 2w
Where l is the length and w is the width.
From the image, the length of the rectangle is 2, and the width is x + 4
So, the perimeter is:
2(2) + 2(x + 4)
= 4 + 2x + 8
= 2x + 8 + 4
= 2x + 12
The Perimeter of the rectangle is 2x + 12
Now, we solve the equation:
12x = 2x + 12
Subtracting 2x from both sides, we have
12x - 2x = 12
10x = 12
Dividing both sides by 10, we have
x = 12/10 or 6/5