ceebs figuring out questions

Rectangle Problem

In this question you are asked to find the area of triangle BEF

So firstly we need to find the dimensions of the rectangle.

P= 2(18)+ 2x

56=36+2x

2x= 20

x=10

Now we know the dimensions

So if we know the area of triangle of ABE and subtract the area of ABF from it, we can find the answer.

That is:

BEF = ABE- ABF

So,

 Area of ABE=  1/2 (18 x 10)

= 90

BEF = ABE- ABF

= 90-42

=48

Hence, the area of triangle BEF is 48.

Question 1

88 children took part in a swimming competition. 1/3 of the boys and 3/7 of the girls wore swimming goggles. Altogether, 34 children wore swimming goggles. How many girls wore swimming goggles on that day?

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Solution:

Let g be the number of girls who did the swimming competition

Let b be the number of boys who did the swimming competition

b + g =88 ----> Equation No.1

1/3b + 3/7g =34 ---->Equation No.2 

1. Multiply Equation No.2 by 3 to get==> b + 9/7g =102

2. In order to subtract Equation No.1 from Equation No.2, multiply Equation No.1 by -1 to get 

-b -g = -88 ---> Equation No. 3

 

3. Now, we are able to cancel out the variable b from both Equation No. 2 and 3

To get 9/7g = 102 --> Equation No.4

           -g= -88  ----> Equation No.5

4. Now we are able to subtract Equation No. 5 from Equation No.4 to get 2/7g = 14

5. We can now go ahead and normally solve the equation for g.....

6. After solving the equation, it is known that the number of girls who completed the swimming competition is 49

7. To find the amount of girls who wore goggles.... find 3/7 of 49

which equals: 21 girls

Traingle question

To find the length of AD, you would have to use the formula of figuring out the perimeter of a rectangle, (2L + 2W). In this case L is 18, thus, 2L is 36. Since there are two variables in the formula and with the addition of one variable being solved, we can algebraically figure out the value of W.
So, 36+2W= 56, then isolate 2W by transposing 36 to the other side, by doing the inverse of +36 which is subtracting 36. So, 2W=56-36.
2W=20. Do the inverse of 2 multiplied by 20, which is dividing 20 by 2.
W=20/2
W=10


The formula of figuring out the area of a triangle is Base multiplied by Height divided by 2 (BH/2)
For the triangle ABE, the height of it is the width of the rectangle, essentially being 10. and the base of the triangle being 18. Substitute the values of B and H. Thus, 18*10/2= 90.
90 being the area of triangle ABE.
To figure out the area of triangle FBE, subtract the area of triangles ABE and ABF (90-42) which gives the answer of 48.
The area of triangle FBE is 48m^2


By Faraj Ahmed SCHS

Rectangle ABCD

1) Figure out 3 other side values from the given 18cm. 

So, all sides added together equal to 56cm. In a rectangle the opposite sides must be the same. So if one side is 18cm, the opposite side will also be 18cm. Then add the two together and minus it from the total. 

18+18 = 36

> 56-36 = 20cm

If you have 20 as rhe answer, all you have to do is divide by two, because you have two remaining sides to find. 

20/2 = 10

So the length values are: 18 and 18

and the width values are 10 and 10

2) Make sure you write down the information already given to you. 

E.g. Total perimeter, triangle areas etc. 

3) The area of the triangle inside ABF is already given to you. This is what we'll use to figure out BEF.

To find BEF we first need to find ABE. 

A= (bxh)/2

A= (18x10)/2

A= 180/2

A= 90cm

4) Taking away 42cm from the total 90cm will give us the area of triangle BEF

90-42= 48

Therefore, triangle BEF= 48cm

  

Solution to Rectangle triangle problem

1. Perimeter of rectangle is 56cm, and AB is 18cm. Therefore dimensions of rectangle is 10cm by 18cm.
2. From this we can figure out the area of triangle AEB, which is 18 times 10, divided by 2, to give 90 cm^2.
3. Triangle AEB consists of triangles AFB and BEF, We know that AFB is 42cm^2 , so to find BEF we subtract ABF from 90, which is 90-42, which will give you 48cm, the area of BEF.

Angus Lye, Solving the maths problem

To find the area of X, we must first identify what values we are given, and how we can use these to solve the problem. We are given the length of the rectangle, 18cm, and its overall perimeter, 56cm. Simple geometry will assure us that from these two values, we can find the value of the side of the rectangle, 10, as on a rectangle both lengths are always the same, and (56-18x2)/2 = 10. Now, these lengths appear seemingly pointless, until we group the two triangles, the uppermost triangle and the triangle we are trying to determine the value of. Once we have done this, we are immediately given two dimensions of the triangle. Its height, 10, is equal to the overall height of the rectangle, and its length, 18, is equal to the overall length of the triangle. To determine the area of the triangle as a whole, we simply use the universal law used to determine the area of a triangle using its height and width, that of A= WxH/2. Once we know the total area of the triangle (10x18/2 = 90), we can simply remove the area of the uppermost original triangle we are given at the start, 42, to leave us with the area of x, 48. We have now solved the problem.
~Angus Lye

hello

hi it's anna anossovitch

HIII EVERYBODY :))

Solution for Question 1

Question 1

88 children took part in a swimming competition. 1/3 of the boys and 3/7 of the girls wore swimming goggles. Altogether, 34 children wore swimming goggles. How many girls wore swimming goggles on that day?
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Solution 

Let b = the number of boys in total that competed in the swimming competition

Let g = the number of girls in total that competed in the swimming competition

b + g = 88 ---> Equation number 1
1/3 b + 3/7 g = 34 ---> Equation number 2

Multiply equation 2 by 3 to get a 'whole number' of boys

b + 9/7 g = 102 ---> Equation number 3

Minus Equation number 1 from equation number 3

2/7 g = 102-88 = 14

The total number of girls = 49

The question asks for the girls that wore swimming goggles - 3/7 of this.

3/7 x 49 = 21

Therefore, 21 girls wore swimming goggles on the day.

(I don't know if Grade 5/6 students will be able to follow this though... but ^^")

Test

I think its working. Sorta Kinda

Rectangle ABCD solution:

1) Write down everything that you know: side lengths and areas.

2) Find the width of the rectangle:

If the perimeter of the rectangle is 56 cm, and the side length of AB is 18cm and DC is 18cm, we can conclude that the lengths of AD and BC is 10cm.

3) Find the area of big triangle (ABE) in the middle (includes shaded and unshaded triangles) by using the formula A=1/2 x b x h. You are given the area of 90cm^2.

4) Subtract the area of the unshaded triangle ABF from the triangle ABE. This can be done as triangle ABF was given the area of 42cm^2.  90cm^2 - 42cm^2 = 48cm^2 for the shaded triangle.

Anna, Nithiya and Sanduni

Test

testing 1,2,3

Sample Questions for the virtual space

Question 1

88 children took part in a swimming competition. 1/3 of the boys and 3/7 of the girls wore swimming goggles. Altogether, 34 children wore swimming goggles. How many girls wore swimming goggles on that day?

Question 2

The ratio of the number of ducks to the number of chickens was 9 : 5. When 20 ducks and 22 chickens were added, the birds were distributed into groups of 7. In each group, there were 4 ducks. Find the number of birds at first.