Question

Calculati aria patratului cu latura de : a) 4,(3) b) 2,(5) c) √8,7 cm d) √3,(7) cm

Answer 1

$\displaystyle a).l=4,(3)= \frac{43-4}{9} = \frac{39}{9}~cm \\ \\ A=l^2=\left( \frac{39}{9} \right)^2= \frac{39^2}{9^2} = \frac{1521}{81} = \frac{169}{9}~cm \\ \\ \boxed{A= \frac{169}{9} ~cm} \\ \\ b).l=2,(5)= \frac{25-2}{9} = \frac{23}{9}~cm \\ \\ A=l^2=\left( \frac{23}{9} \right )^2= \frac{23^2}{9^2} = \frac{529}{81} ~cm \\ \\ \boxed{A= \frac{529}{81} ~cm}$

$\displaystyle c).l= \sqrt{8,7} = \sqrt{ \frac{87}{10} } = \frac{ \sqrt{87} }{ \sqrt{10} }~cm \\ \\ A=l^2=\left( \frac{ \sqrt{87} }{ \sqrt{10} } \right)^2= \frac{ \sqrt{87}^2 }{ \sqrt{10} ^2} = \frac{87}{10} ~cm \\ \\ \boxed{A= \frac{87}{10} ~cm}$

$\displaystyle d).l= \sqrt{3,(7)} = \sqrt{ \frac{37-3}{9} } = \sqrt{ \frac{34}{9} }= \frac{ \sqrt{34} }{ \sqrt{9} } = \frac{ \sqrt{34} }{3} ~cm \\ \\ A=l^2=\left( \frac{ \sqrt{34} }{3} \right)^2= \frac{ \sqrt{34} ^2}{3^2} = \frac{34}{9} ~cm \\ \\ \boxed{A= \frac{34}{9} ~cm}$