Răspuns:
Explicație pas cu pas:
1.
d^2 = l^2 + l^2 = 2l^2
d = l√2
2.
d = l√2
a) 4√2 cm
b) 18√2 cm
c) 7√6 cm
d) 18 cm
3.
d = l√2
l =d/√2 = d√2/2
a) 12√2*√2/2 = 12 cm
b) 10√2/2 = 5√2 cm
c) 24√3*√2/2 = 12√6 cm
d) 9√10*√2/2 = 9√20/2 = 9*2√5/2 = 9√5 cm
4.
h^2 = l^2 - (l/2)^2 = l^2 - l^2/4 = 4l^2/4 - l^2/4 = 3l^2/4
h = l√3/2
5.
h = l√3/2
a) 8*√3/2 = 4√3 cm
b) 6√3*√3/2 = 9 cm
c) 15√2*√3/2 = 15√6/2 cm
d) 8√3/3*√3/2 = 4 cm
6.
h = l√3/2
l = 2h/√3 = 2h√3/3
a) 2*14√3*√3/3 = 28 cm
b) 2*6√3/3 = 4√3 cm
c) 2*18√2*√3/3 = 12√6 cm
d) 2*15√6*√3/3 = 30√2 cm
8.
Triunghi dreptunghic isoscel = fiecare cateta are 12 cm
I = ipotenuza
I^2 = 12^2 + 12^2 = 144 + 144 = 288
I = √288 = 12√2 cm
9.
I^2 = C^2 + C^2 = 2C^2
C^2 = I^2/2
C = I/√2 = I√2/2 = 8√3*√2/2 = 4√6 cm
