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cwrw238

  • 3 years ago

Find ratio of area of p to area of q.

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  1. cwrw238
    • 3 years ago
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    |dw:1341591452831:dw|

  2. eyust707
    • 3 years ago
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    well they are both just triangles minus the same little corner...

  3. cwrw238
    • 3 years ago
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    The whole figure is a square and the line bisects the right side of the square. this question was from a maths paper for 16 year old's. I would have struggled to do this at 16 - probably would have given up.

  4. eyust707
    • 3 years ago
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    |dw:1341591736170:dw| p = (1*2)/2 - A q= (2*2)/2 - A Subtracting the same amount from both wont effect the ratio, so: p:q = 1/2

  5. eyust707
    • 3 years ago
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    *i think*** lol i havent taken geometry since 10th grade

  6. eyust707
    • 3 years ago
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    haha thats a cool one though!

  7. eyust707
    • 3 years ago
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    What do you think does my logic seem sound?

  8. cwrw238
    • 3 years ago
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    no - thats not the answer

  9. eyust707
    • 3 years ago
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    hmm maybe you can tjust take off the A

  10. eyust707
    • 3 years ago
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    but if we find that little A we are golden

  11. cwrw238
    • 3 years ago
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    yes

  12. eyust707
    • 3 years ago
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    I could do it using trig but thats a pain and I know there's an easier way...

  13. cwrw238
    • 3 years ago
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    i did it differently using systems of equations there maybe an easier way though this is how i started

  14. cwrw238
    • 3 years ago
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    |dw:1341592406267:dw|

  15. phi
    • 3 years ago
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    |dw:1341592415019:dw| we can label the sides of the square 1 for easy calculation. similar triangles p and x, with x scaled by 1/2 means the area of x is 1/4 of p the rest of the areas are easy to find.

  16. cwrw238
    • 3 years ago
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    area x : area y = 1^2 : 2^2 = 1: 4 then i got 4 equations in x, y , p and q and splved - a bit messy !!

  17. cwrw238
    • 3 years ago
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    yea - i think thats a bit better way than mine

  18. eyust707
    • 3 years ago
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    haha phi isnt that just the same problem again... |dw:1341592696668:dw|

  19. phi
    • 3 years ago
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    the altitudes are also in ratio of 1/2 so p's alt is 1/3 and x's is 1/6 as they add to 1/2

  20. cwrw238
    • 3 years ago
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    yes

  21. phi
    • 3 years ago
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    so find the area of p, area of q is (1/2)^2 + (1/2)*(1/2)^2 + area(x)

  22. cwrw238
    • 3 years ago
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    so q = 1/4 + 1/8 + area(x) = 3/8 + area(x)

  23. phi
    • 3 years ago
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    area(x)= (1/2)*(1/2)*(1/6)= 1/24 area(p)= (1/2)*1*(1/3)= 1/6

  24. phi
    • 3 years ago
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    so ratio of areas p/q = 2/5

  25. cwrw238
    • 3 years ago
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    i got 2: 5 area p = 1/6 area q = 3/8 + 1/24 = 10/24 = 5/12 p/q = 1/6 * 12/5 = 12/60 = 2/5 - yea

  26. cwrw238
    • 3 years ago
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    - quite a searching question for 16 year old, i thought

  27. cwrw238
    • 3 years ago
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    - thanx

  28. phi
    • 3 years ago
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    Back in the old days, maybe they worked harder at this stuff??

  29. cwrw238
    • 3 years ago
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    yea - good point!

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