MO-Z5-3-66 tiles

The picture shows a square tiles with side 10 dm which is composed of four identical small rectangles and squares. Circumference of small square is five times smaller than the circumference of the entire tile. Determine the dimensions of the rectangle.

Correct result:

x =  40 cm
y =  60 cm

Solution:

a=10 10=100 b=a/5=100/5=20 a=2x+b x=(ab)/2=(10020)/2=40 cma=10 \cdot \ 10=100 \ \\ b=a/5=100/5=20 \ \\ a=2x+b \ \\ x=(a-b)/2=(100-20)/2=40 \ \text{cm}
a=x+y y=ax=10040=60 cma=x+y \ \\ y=a-x=100-40=60 \ \text{cm}



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