Circumscribed 2671

The circle's radius circumscribed by the rectangle is 5 cm, and one side of the rectangle is 6 cm long. Calculate the length of the other side and the area of the rectangle.

Correct answer:

b =  8 cm
S =  48 cm²

Step-by-step explanation:

$$\begin{gathered} r=5\text{cm} \\ a=6\text{cm} \\ {r}^2=(a/2{)}^2+(b/2{)}^2 \\ b=2\cdot \sqrt{r^2-(a/2{)}^2}=2\cdot \sqrt{5^2-(6/2{)}^2}=8\text{cm} \end{gathered}$$

$S=6\cdot b=6\cdot 8=48{\text{cm}}^2$

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