Problem 5.5. A large rectangle consists of three identical squares and three identical small rectangles. The perimeter of the square is 24, and the perimeter of the small rectangle is 16. What is the perimeter of the large rectangle?

The perimeter of a figure is the sum of the lengths of all its sides.

![](https://cdn.mathpix.com/cropped/2024_05_06_d3a039ae044fd2dec0bcg-09.jpg?height=238&width=547&top_left_y=951&top_left_x=453)
Answer: 52.

Solution. All sides of a square are equal, and its perimeter is 24, so each side is $24: 4=6$. The perimeter of the rectangle is 16, and its two largest sides are each 6, so the two smallest sides are each $(16-6 \cdot 2): 2=2$. Then the entire large rectangle has dimensions $8 \times 18$, and its perimeter is $2 \cdot(8+18)=$ 52.