victorlau123
Perimeter of one triangle is 11/13 of the perimeter of a similar triangle. The difference of the lengths of two corresponding sides is 1m. What are the lengths of these sides?
Delete
Share
This Question is Closed
sauravshakya
Best Response
You've already chosen the best response.
2
|dw:1358609419748:dw| LET THAT TWO TRIANGLES BE SIMILAR
sauravshakya
Best Response
You've already chosen the best response.
2
(a+b+c)/(a'+b'+c')=11/13
victorlau123
Best Response
You've already chosen the best response.
0
@hero
victorlau123
Best Response
You've already chosen the best response.
0
What do I do next? I get what you are doing
sauravshakya
Best Response
You've already chosen the best response.
2
u mean difference of all three corresponding sides are 1m or only difference of one corresponding sides is 1m
victorlau123
Best Response
You've already chosen the best response.
0
pair of corresponding sides.
sauravshakya
Best Response
You've already chosen the best response.
2
So, all
a'-a=1 ====>a'=a+1
b'-b=1====>b'=b+1
c'-c=1====>c'=c+1
victorlau123
Best Response
You've already chosen the best response.
0
yep
victorlau123
Best Response
You've already chosen the best response.
0
difference between one corresponding sides is 1m
sauravshakya
Best Response
You've already chosen the best response.
2
U mean only a'-a=1
NOT all
victorlau123
Best Response
You've already chosen the best response.
0
yes
victorlau123
Best Response
You've already chosen the best response.
0
that is correct
sauravshakya
Best Response
You've already chosen the best response.
2
(a+b+c)/(a'+b'+c')=11/13
13a+13b+13c=11a'+11b'+11c'
(13a-11a') + (13b-11b') + (13c-11c')=0
a (13-11a'/a) +b (13-11b'/b) +c(13-11c'/c)=0
Now,
a'/a =b'/b =c'/c = (1+a)/a
So,
(a+b+c) {13-11(1+a)/a}
sauravshakya
Best Response
You've already chosen the best response.
2
Similarly,
a'(13a/a' -11) + b'(13b/b' -11) +c' (13c/c' -11)=0
(a'+b'+c') { 13a/(a+1) -11}=0
sauravshakya
Best Response
You've already chosen the best response.
2
So,
(a+b+c) {13-11(1+a)/a}/(a'+b'+c') { 13a/(a+1) -11}=0
{13 -11(1+a)/a}=0
13a-11-11a=0
2a=11
a=5.5
sauravshakya
Best Response
You've already chosen the best response.
2
So, is it 5.5 and 6.5
sauravshakya
Best Response
You've already chosen the best response.
2
NOTE: I assumed a'-a=1
victorlau123
Best Response
You've already chosen the best response.
0
Thanks
sauravshakya
Best Response
You've already chosen the best response.
2
welcome