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victorlau123 Group Title

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?

  • one year ago
  • one year ago

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  1. sauravshakya Group Title
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    |dw:1358609419748:dw| LET THAT TWO TRIANGLES BE SIMILAR

    • one year ago
  2. sauravshakya Group Title
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    (a+b+c)/(a'+b'+c')=11/13

    • one year ago
  3. victorlau123 Group Title
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    @hero

    • one year ago
  4. victorlau123 Group Title
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    What do I do next? I get what you are doing

    • one year ago
  5. sauravshakya Group Title
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    u mean difference of all three corresponding sides are 1m or only difference of one corresponding sides is 1m

    • one year ago
  6. victorlau123 Group Title
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    pair of corresponding sides.

    • one year ago
  7. sauravshakya Group Title
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    So, all a'-a=1 ====>a'=a+1 b'-b=1====>b'=b+1 c'-c=1====>c'=c+1

    • one year ago
  8. victorlau123 Group Title
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    yep

    • one year ago
  9. victorlau123 Group Title
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    difference between one corresponding sides is 1m

    • one year ago
  10. sauravshakya Group Title
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    U mean only a'-a=1 NOT all

    • one year ago
  11. victorlau123 Group Title
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    yes

    • one year ago
  12. victorlau123 Group Title
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    that is correct

    • one year ago
  13. sauravshakya Group Title
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    (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}

    • one year ago
  14. sauravshakya Group Title
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    Similarly, a'(13a/a' -11) + b'(13b/b' -11) +c' (13c/c' -11)=0 (a'+b'+c') { 13a/(a+1) -11}=0

    • one year ago
  15. sauravshakya Group Title
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    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

    • one year ago
  16. sauravshakya Group Title
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    So, is it 5.5 and 6.5

    • one year ago
  17. sauravshakya Group Title
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    NOTE: I assumed a'-a=1

    • one year ago
  18. victorlau123 Group Title
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    Thanks

    • one year ago
  19. sauravshakya Group Title
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    welcome

    • one year ago
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