Question

Aflati înălțimea si aria unui triunghi echilateral cu latura de :
A. 2 CM
B. 100 CM
C. radical din 3 cm
D. 3 pe 2 cm
E. 1+ radical din 2 cm
F. 2a



Va rog repede sau coroana

Answer 1

Mentionez ca formulele de aflare a inaltimii si ariei sunt:

$h = \frac{l \sqrt{3} }{2}$
$aria = \frac{ {l}^{2} \sqrt{3} }{4}$
A. l = 2 cm
$h = \frac{2 \sqrt{3} }{2} \\ a = \frac{ {2}^{2} \sqrt{3} }{4} = \sqrt{ 3}$
B. 100cm
$h = \frac{100 \sqrt{3} }{2} = 50 \sqrt{3} \\ aria = \frac{ {100}^{2} \sqrt{3} }{4} = 2500 \sqrt{3}$

C. l = rad din 3

$h = \frac{ \sqrt{3} \sqrt{3} }{2} = \frac{3}{2}$
$aria = \frac{ { \sqrt{3} }^{2} \sqrt{ 3} }{4} = \frac{3 \sqrt{3} }{4}$
D.

$h = \frac{ \frac{3}{2} \sqrt{3} }{2} = \frac{3 \sqrt{3} }{4} \\ aria = \frac{ { \frac{3}{2} }^{2} \sqrt{3} }{4} = \frac{9 \sqrt{3} }{16}$
E.
$h = \frac{(1 + \sqrt{2}) \sqrt{3} }{2} = \frac{ \sqrt{3} + \sqrt{6} }{2} \\ aria = \frac{ {(1 + \sqrt{2}) }^{2} \sqrt{3} }{4} = \frac{3 \sqrt{3} + 2 \sqrt{6} }{4}$
F. 2a
$h = \frac{2a \sqrt{3} }{2} = a \sqrt{3} \\ aria = \frac{(2a)^{2} \sqrt{3} }{4} = \frac{4 {a}^{2} \sqrt{3} }{4} = {a}^{2} \sqrt{3}$