3. Rectangle $A B C D$ consists of 6 shapes similar to the letter "L", and each "L" shape consists of 4 equal squares. If the sum of the perimeters of all the "L" shapes is $1200 \mathrm{~mm}$, what is the perimeter of rectangle $A B C D$?

![](https://cdn.mathpix.com/cropped/2024_06_03_6e1b38aefafca10e6d1eg-3.jpg?height=360&width=457&top_left_y=1650&top_left_x=317)
3. Rectangle $A B C D$ consists of 6 shapes similar to the letter "L", and each "L" shape consists of 4 equal squares. If the sum of the perimeters of all the "L" shapes is 1200 mm, what is the perimeter of rectangle $A B C D$?

## Solution.

![](https://cdn.mathpix.com/cropped/2024_05_30_0b00c6f52e60bdba44a4g-08.jpg?height=340&width=420&top_left_y=841&top_left_x=1383)

The perimeter of one "L" shape is 1200 : $6=200 \mathrm{~mm}$.

Let $a$ be the side length of the square from which the "L" shape is composed.

The perimeter of the "L" shape is $10 a$.

1 POINT

We have $10 a=200$,

or $a=20 \mathrm{~mm}$

1 POINT

The lengths of the sides of the rectangle are:

| $6 a=6 \cdot 20=120 \mathrm{~mm}$ | $1 \mathrm{POINT}$ |
| :--- | ---: |
| $4 a=4 \cdot 20=80 \mathrm{~mm}$ | $1 \mathrm{POINT}$ |
|  |  |
| The perimeter of rectangle $A B C D$ is $2 \cdot 120+2 \cdot 80=400 \mathrm{~mm}$. | 1 POINT |
| ............................................................................................. |  |