Question

Un paraleogram ABCD, are diagonala AC perpend. AB si laturile AB = 15 cm si BC = 25 cm. Calculati aria paralelogramului.

Answer 1

$Aplicam ~teorema ~lui~Pitagora ~in ~triunghiul~ABC: \\ AB^2=AC^2+BC^2 \Rightarrow 15^2=AC^2+25^2 \Rightarrow 225=AC^2+625 \Leftrightarrow \\ \Leftrightarrow AC^2=625-225 \Rightarrow AC^2=400 \Rightarrow AC= \sqrt{400} \Rightarrow AC=20~cm \\ A_{ABCD}=AB \cdot AC=15 \cdot 20=300~cm^2$