5. Four equal rectangles are arranged to form a larger rectangle as shown in the figure. Calculate the perimeter and area of the larger rectangle if the perimeter of each smaller rectangle is $4 \mathrm{dm}$.

![](https://cdn.mathpix.com/cropped/2024_06_03_abe7066be769a83bc601g-1.jpg?height=309&width=416&top_left_y=2164&top_left_x=800)

Each problem is scored out of 10 points.

The use of a pocket calculator or any reference materials is not allowed.

Ministry of Science, Education and Sports of the Republic of Croatia

Agency for Education and Upbringing

Croatian Mathematical Society

## REGIONAL MATHEMATICS COMPETITION
5. From the image, it is visible that the length of the smaller rectangle is three times greater than its width. Let the sides of the smaller rectangle be $a$ and $3a$.

It holds: $2 \cdot 3a + 2 \cdot a = 40$, so $a = 5 \text{ cm}$.

2 POINTS

The sides of the larger rectangle are $4a$ and $3a$, i.e., $20 \text{ cm}$ and $15 \text{ cm}$.

2 POINTS

The perimeter of the larger rectangle is

$o = 2 \cdot 20 + 2 \cdot 15$,

$o = 70 \text{ cm}$.

2 POINTS

The area of the larger rectangle is

$p = 20 \cdot 15$,

$p = 300 \text{ cm}^2$.

## SOLUTIONS FOR 5th GRADE

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