Calculate 70814

The lengths of the sides AB and AD of the rectangle ABCD are in the ratio 3:4. A circle k with a diameter of 10 cm describes a rectangle. Calculate the side lengths of a given rectangle.

Correct answer:

a =  12 cm
b =  16 cm

Step-by-step explanation:

$$\begin{gathered} a:b=3:4 \\ r=10\text{cm} \\ r=u/2=\sqrt{a^2+b^2}/2 \\ 4r^2=a^2+b^2 \\ 4r^2=(3/4\cdot b{)}^2+b^2 \\ 4r^2=(9/16+1)\cdot b^2 \\ b=\sqrt{4\cdot r^2/(9/16+1)}=\sqrt{4\cdot 10^2/(9/16+1)}=16\text{m} \\ a=3/4\cdot b=3/4\cdot 16=12\text{cm} \end{gathered}$$

$$\begin{gathered} b=16=16\text{cm} \\ \text{ Verifying Solution: } \\ {r}_2=\sqrt{a^2+b^2}/2=\sqrt{12^2+16^2}/2=10\text{cm} \end{gathered}$$

Try another example