$$r=1 dm = 10 cm$$

$$a:b=3:4$$

$$a^2+b^2={\left(2r\right)}^2$$

$$3b=4a$$

$$b=\frac{4}{3}a$$

$$a^2+b^2={\left(2·10\right)}^2$$

$$a^2+b^2=400$$

$$a^2+{\left(\frac{4}{3}a\right)}^2=400$$

$$a^2+\frac{16a^2}{9}=400 |·9$$

$$9a^2+16a^2=3600$$

$$25a^2=3600$$

$$a^2=\frac{3600}{25}$$

$$a^2=144$$

$$a=\sqrt{144}$$

$$a=12 cm$$

$$b=16 cm$$

$$P=12·16$$

$$P=192 c{m}^2$$