Wednesday, July 14, 2010

Ratio P6

In the figure below, which is not drawn to scale, 1/3 of the circle is shaded, 1/5 of the triangle is shaded and 1/4 of the rectangle is shaded. The total area of the circle and triangle is 7/8 of the rectangle. Given that the total area of the whole figure is 260 cm2, find the area of the rectangle.















C + T : R = 7 : 814 : 16  Multiply by 2 to make (C + T) the same
7 x ? = 3 x ? + 5 x ?  [7 x 2 = 3 x 3 + 5 x 1 Guess and Check]

CS : C = 1 : 3 = 3 : 9   Multiply by 3 to make (C + T) the same

TS : T = 1 : 5

RS : R = 1 : 4 = 4 : 16  Multiply by 4 to get R = 16

C + T + R --> 14 + 16 - 3 - 1 = 26

26 u --> 260
1 u --> 260/26 = 10

16 u --> 16 x 10 = 160 cm2.

The area of the rectangle is 160 cm2.



Alternative method [Given informations 1/3 and 1/5 are redundant]

C + T : R = 7 : 8

RS : R = 1 : 4 = 2 : 8

7 + 8 - 2 = 13    Minus 2 to remove double-counting of shaded areas.

13 u --> 260
1 u --> 260/13 = 20

8 u --> 8 x 20 = 160 cm2.

The area of the rectanglee is 160 cm2.

4 comments:

  1. Obs, I have tried to understand your solution but the thing is that i still don't know how to use addition and multiplication on problem sum....

    Refer to link for examples...and hope you can enlighten me when we should use addition and multiplication...

    Example 1

    http://4.bp.blogspot.com/_NGNaLTzN5_U/SQxTRczo6vI/AAAAAAAAA-o/TN0PwcEVk80/s1600-h/MathsChallengingQ010.JPG


    Example 2

    http://4.bp.blogspot.com/_NGNaLTzN5_U/SQxR1BQlCgI/AAAAAAAAA9I/Ozy-G5mWrWQ/s1600-h/MathsChallengingQ002a.JPG

    http://2.bp.blogspot.com/_NGNaLTzN5_U/SnJh1OoNA6I/AAAAAAAACWc/zD_Mpyr-0Ak/s1600-h/MathsP4NYSA2Q45ChallengingAb.JPG

    In example 2, why multiply instead of addition?


    Example 3


    http://3.bp.blogspot.com/_NGNaLTzN5_U/SQxR00tZgEI/AAAAAAAAA9A/k1PUrm6Rxqg/s1600-h/MathsChallengingQ002b.JPG

    In example 3, why you add instead of multiply?

    ReplyDelete
  2. Please look at the remarks in the red box.

    Another way is for you to list them out and you will be able to see clearly.


    For example 3, besides addition, I have also shown how to can use multication - 20 x 19 / 2 [You need to divide by 2 because when A shakes hand with B or B with A, they are actually the same].


    You may want to use the method taught in your school .

    ReplyDelete
  3. But how do you identify whether addition and multiplication from a question?

    ReplyDelete
  4. It does not depend on the question. It depends on what method you are using to solve the question. Please go through the comments in red box. Try to make a list of the different ways using less number. You will be able to appreciate better why add or multiply.

    This was taught at Sec 3 (Additional Maths) during my school day. So obviously, we have less problem to understand.

    ReplyDelete