Question

Un triunghi isoscel are aria de 1092 cm^2 si inaltimea din varf de 13 cm.Calculeaza lungimile celorlalte doua inaltimi.Va rog este urgent.​

Answer 1

Fie b lungimea bazei, h inaltimea si $h_2$ inaltimea care trebuie aflata

$A = \frac{b\cdot h}{2}$

$b = \frac{2A}{h}$

$Latura = \sqrt{(\frac{b}{2}) ^ 2 + h^2} = \sqrt{\frac{b^2}{4} + h^2} = \sqrt{\frac{b^2 + 4h^2}{4}} = \frac{\sqrt{b^2 + 4h^2}}{\sqrt{4}} = \frac{\sqrt{b^2 + 4h^2}}{2} = \frac{\sqrt{(\frac{2A}{h})^2 + 4h^2}}{2} = \frac{\sqrt{\frac{4A^2}{h^2} + 4h^2}}{2} = \frac{\sqrt{\frac{4A^2 + 4h^4}{h^2}}}{2} = \frac{\sqrt{\frac{4}{h^2}\cdot (A^2 + h^4)}}{2} = \frac{2\sqrt{A^2 + h^4}}{2h} = \frac{\sqrt{A^2 + h^4}}{h} = \frac{\sqrt{1192464 + 28561}}{13} = \frac{\sqrt{1221025}}{13} = \frac{1105}{13} = 85\:cm$

$85 = \frac{2A}{h_2} = \frac{2184}{h_2}\rightarrow h_2 = \frac{2184}{85} = 25.69\:cm$