Answer:
The perimeter of the small square is approximately 9.154 units
Step-by-step explanation:
The given parameters are;
The sides of the four identical right triangles = 5·x, 12·x, and 13·x,
The perimeter of the large square = 17 units
Therefore, we have;
The hypotenuse side of the right triangles = The longest side = 13·x
The sides of the large square are formed by the hypotenuse sides of the right triangle
Therefore, the perimeter of the large square = 4 × 13·x = 52·x = 17 units
x = 17/52 ≈ 0.3269
x ≈ 0.3269 units
The sides of the small square = The difference between the longer and the shorter of the two legs = 12·x - 5·x = 7·x
∴ The sides of the small square = 7·x = (7 × 0.3269) units ≈ 2.2885 units
The perimeter of the small square = 4 × The sides of the small square
The perimeter of the small square ≈ (4 × 2.2885) units ≈ 9.154 units
The perimeter of the small square ≈ 9.154 units.
