Squares ratio

The first square has a side length of a = 6 cm. The second square has a circumference of 6 dm. Calculate the proportions of the perimeters and the proportions of these squares. (Write the ratio in the basic form). (Perimeter = 4 * a, area S = a²)

Correct answer:

r₁ =  2:5
r₂ =  4:25

Step-by-step explanation:

$$\begin{gathered} a=6\text{cm} \\ {o}_2=6\text{dm}\to \text{cm}=6\cdot 10\text{cm}=60\text{cm} \\ {o}_2=4b \\ b=o_2/4=60/4=15\text{cm} \\ {o}_1=4\cdot a=4\cdot 6=24\text{cm} \\ {r}_1=o_1/o_2=24/60=0.4=2:5 \end{gathered}$$

$$\begin{gathered} S_1=a^2=6^2=36{\text{cm}}^2 \\ {S}_2=b^2=15^2=225{\text{cm}}^2 \\ {r}_2=S_1/S_2=36/225=0.16=4:25 \end{gathered}$$

Try another example