The perimeter of the shape in the image is 12 inches.
To find the perimeter, we add up the lengths of all the sides. The sides of the shape are: a inches , 3t inches ,4a inches ,2t inches
Adding these up, we get:
Perimeter = a + 3t + 4a + 2t
Simplifying, we get:
Perimeter = 5a + 5t
Since the sides are all equal in length, we can substitute 41/4 inches for a and t. This gives us:
Perimeter = 5(41/4) + 5(41/4)
Simplifying, we get:
Perimeter = 102.5 + 102.5
Therefore, the perimeter of the shape is 12 inches.
Explanation in detail:
The perimeter of a shape is the total length of all its sides added together.
In the image, the shape is made up of four sides: a, 3t, 4a, and 2t.
To find the perimeter of the shape, we simply add up the lengths of all four sides.
Perimeter = a + 3t + 4a + 2t
We can then simplify this expression by combining like terms:
Perimeter = (1 + 4)a + (3 + 2)t
Perimeter = 5a + 5t
Since the sides of the shape are all equal in length, we can substitute 41/4 inches for a and t. This gives us:
Perimeter = 5(41/4) + 5(41/4)
Simplifying, we get:
Perimeter = 102.5 + 102.5
Therefore, the perimeter of the shape is 12 inches