Question

Un dreptunghi are latimea 3/5 din lungime si aria 1215 m patrati.Sa se afle perimetrul dreptunghiului

Answer 1

l = 3L/5
A = L × l = 1215 m^2
L × 3L/5 = 1215
3L^2 = 1215 × 5
3L^2 = 6075
L^2 = 6075 : 3
L^2 = 2025
L = 45 m (lungimea)
l = 3 × 45/5 = 3 × 9 = 27 m (latimea)
P = 2 ×(45 + 27) = 2 × 72 = 144 m
P = 144 m

Verificare:
45 × 27 = 1215 m^2

Answer 2

$l = \dfrac{3}{5}\cdot L m\\ \\ \left\{ \begin{array}{c} A_{\boxed{~}} = l\cdot L m^2}\quad \\ A_{\boxed{~}} = 1215 m^2 \end{array} \right| \Rightarrow \left\{ \begin{array}{c} l\cdot L = 1215 m^2}\\l=\dfrac{3}{5}\cdot L m\quad \end{array} \right| \Rightarrow \dfrac{3}{5}\cdot L\cdot L = 1215 m^2 \Rightarrow \\ \\ \\ \Rightarrow \dfrac{3}{5}\cdot L^2 = 1215 m^2 \Rightarrow L^2 = \dfrac{1215\cdot 5}{3} m^2 \Rightarrow L^2 = 405\cdot 5 m^2 \Rightarrow$

$\Rightarrow L^2 = 81\cdot 5\cdot 5 m^2 \Rightarrow L^2 = 9^2\cdot 5^2 m^2 \Rightarrow L = 9\cdot 5 m \Rightarrow L=45 m \Rightarrow \\ \\ \Rightarrow\left\{ \begin{array}{c} L = 45 m \\ l=\dfrac{3}{5}\cdot L m \end{array} \right \Rightarrow \left\{ \begin{array}{c} L = 45 m \\ l=\dfrac{3}{5}\cdot 45 m\end{array} \right \Rightarrow \left\{ \begin{array}{c} L = 45 m \\ l=27 m\end{array} \right |$

$P_{\boxed{~}} = 2\times(L+l) m \Rightarrow P_{\boxed{~}} = 2\times(45+27) m \Rightarrow\\ \\ \Rightarrow P = 2\times 72 m \Rightarrow \boxed{P_{\boxed{~}} = 144\text{ m}}$