Question

Dau coroana! Doar ex 9 si 13.Va rog explicați!

Answer 1

9.
a)a/3=b/4=c/6=k
a=3k
b=4k
c=6k
3k+4k+6k=104
13k=104 =>k=8
=>a=24
=>b=32
=>c=48

b)a/2=5b/16=4c=k
a=2k
b=16k/5
c=k/4
4k + 16k/5 - k/4 = 278
Numitor comun 20
80k+64k-5k=278
139k=278 =>k=2
=>a=4
=>b=32/5
=>c=1/2

c)3a=5b/3=c/2=k
a=k/3
b=3k/5
c=2k
k - 3k/5 + 4k = 22/25
Numitor comun 25
25k-15k+100k=22
110k=22 =>k=22/110=2/10=1/5
=>a=1/15
=>b=3/25
=>c=2/5

d)2a=3b/2=2c/3=k
a=k/2
b=2k/3
c=3k/2
4k²/9 + 9k²/4 - k²/4 = 11/18
Numitor comun 36
16k²+81k²-9k²=11
88k²=11 =>k²=11/88 =>k²=1/8 =>k=1/2√2=√2/4
=>a=√2/8
=>b=√2/6
=>c=3√2/8

13.
L/20=l/16=k
L=20k
l=16k
P=2L+2l=54
40k+32k=54
72k=54  l:18
4k=3 =>k=3/4
=>L = 3/4 · 20 = 15 cm
=>l = 3/4 · 16 = 12 cm
Aria=15·12=180 cm²