• Join over 1.2 million students every month
• Accelerate your learning by 29%
• Unlimited access from just £6.99 per month
Page
1. 1
1
2. 2
2
3. 3
3
4. 4
4
5. 5
5
6. 6
6
7. 7
7
8. 8
8
9. 9
9
10. 10
10
11. 11
11
12. 12
12
13. 13
13
14. 14
14
15. 15
15
16. 16
16
17. 17
17

# Investigate the relationships between the lengths of the 3 sides of the right angled triangles and the perimeters and areas of these triangles.

Extracts from this document...

Introduction

Kamran Ali 10.1                GCSE Maths Coursework

Aim: To investigate the relationships between the lengths of the 3 sides of the right angled triangles and the perimeters and areas of these triangles.

a)

The numbers 5, 12, 13 satisfy the condition.

5² + 12² = 13²

Because 5² = 5x5 = 25

12² = 12x12 = 144

13² = 13x13 = 169

And so

5² + 12² = 25 + 144 = 169 = 132

b)

The Numbers 7, 24, 25 also satisfy the condition.

7² + 24² =25²

Because  7² = 7x7 = 49

24² = 24x24 = 576

25² = 25x25 = 525

And so

7² + 24² = 49+ 576 = 625 = 25²

Task2: The perimeter and area of the triangle are:

a)

b)

 Length of shortest side Length of middle side Length of longest side Perimeter Area 3 4 5 12 6 5 12 13 30 30 7 24 25 84 84

Length of short side is going to be in fixed steps meaning that this is a linear sequence and the length of middle side and longest side is actually a quadratic sequence because they are not in fixed steps and in geometric sequence.

4     , 12     , 24     , 40

8     , 12     , 16

4     , 4

5     , 13     , 25     , 41

8     , 12     , 16

1. , 4

Length of shortest side:

 Term no 1 2 3 4 5 Sequence 3 5 7 9 11 Sequence 2n 1 4 6 8 10 Sequence 1 1 1 1 1

Middle

I am doing this to eliminate C from these equations

9a + 3b + c = 24 –eqn3

-  4a + 2b + c = 12 –eqn2

5a + b          = 12 –eqn4

Equation 2 – Equation 1

I am doing this to eliminate C and form a fifth equation that I will subtract with equation 4.

4a + 2b + c = 12 –eqn2

-  a + b + c = 4 –eqn1

3a + b          = 8 –eqn5

Equation 4 – Equation 5

I am doing this to eliminate B and finally work out what A is worth.

5a + b = 12 –eqn4

-  3a + b = 8 –eqn5

2a          = 4

A = 4/2

A = 2

Substitute A =2 into equation 5

I am doing this to find what B is worth.

3a + b = 8

3 x 2 + b = 8

6 + b = 8

B = - 6

B = 2

Substitute A =2 and B = 2 into equation 1.

I am doing this to find what C is worth.

A + B + C = 4

2 + 2 + C = 4

4 + C       = 4

C = 0

F (n) = an² + bn + c

F (n) = 2n² + 2n

Try n = 1

F (1) = 2 x 1² + 2 x 1

= 2 + 2

= 4

Try n = 2

F (2) = 2 x 2² + 2 x 2

= 8 + 4

= 12

Try n = 100

F (100) = 2 x 100² + 2 x 100

= 10000 + 200

= 20200

Length of longest side:

F (n) = an² + bn +c

F= (1) = a x 1² + b x 1 + c

= a + b + c = 5 – eqn1

F= (2)

Conclusion

-  a + b + c + d = 6 –eqn1

7a + 3b + c      = 24- eqn7

Equation 6 – Equation 7

I am doing this to eliminate C.

19a + 5b + c = 54 –eqn6

-  7a + 3b + c = 24- eqn7

12a + 2b       = 30- eqn8

Equation 5 – Equation 6

I am doing this to eliminate C.

37a + 7b + c = 96 –eqn5

-  19a + 5b + c = 54 –eqn6

18a + 2b       = 42- eqn9

Equation 9 – Equation 8

I am doing this to eliminate B and to find the value of A is worth.

18a + 2b       = 42- eqn9

-    12a + 2b       = 30- eqn8

6a                      = 12

A = 12/6

A = 2

Substitute A = 2 into equation 9.

I am doing this to find what B is worth.

12a + 26 = 30

12 x 2 + 2b = 30

24 + 2b = 30

2b = 30 – 24

2b = 6

b = 6/2

B=3

Substitute A = 2 and B = 3 into equation 6.

I am doing this to find what C is worth.

19a + 5b + c = 54

19 x 2 + 5 x 3 + c = 54

38 + 15 + c = 54

53 + 15 + c = 54

c = 54 – 53

C = 1

Substitute A = 2 and B = 3 and C = 1 into equation 1.

I am doing this to find what D is worth.

A + B + C + D = 6

2 + 3 + 1 + D = 6

6 + D = 6

D = 6 – 6

D = 0

F (n) = a³ + bn² + cn + d

F (n) = 2n³ + 3n² + n

Try n = 1

F (1) = 2 x 1³ + 3 x 1² + 1 x 1

= 2 + 3 + 1

= 6

Try n = 2

F (2) = 2 x 2³ + 3 x 2² + 1 x 2

= 16 + 12 + 2

= 30

By:

Kamran Ali 10.1

Kamran Ali 10.1                GCSE Maths Coursework

This student written piece of work is one of many that can be found in our AS and A Level Core & Pure Mathematics section.

## Found what you're looking for?

• Start learning 29% faster today
• 150,000+ documents available
• Just £6.99 a month

Not the one? Search for your essay title...
• Join over 1.2 million students every month
• Accelerate your learning by 29%
• Unlimited access from just £6.99 per month

# Related AS and A Level Core & Pure Mathematics essays

1. ## Functions Coursework - A2 Maths

a root of the equation f(x)=0 lies in the interval [1.87,1.88]. The rest of the method could also be illustrated graphically in this way. The next table show values of f(x) at values of x from 1.87 to 1.88, with intervals of 0.001.

2. ## Mathematics Coursework - OCR A Level

6.106E-16 0.2503 2.776E-16 0.2503 1.11E-16 0.2503 5.551E-17 0.2503 0 0.2503 0 Above it is clear that the solution is 0.2503 (to 4 significant figures) as the difference between x and y at this point is 0. Using Autograph does not give us more 4 significant figures though which is insufficient.

1. ## Arctic Research (Maths Coursework)

= distance (d) / time (t) to find the time it would take, ignoring the wind, for one journey. If we multiply this result by 16 it will give us a fair idea of time it should take for all the 16 flights.

2. ## Solutions of equations

x F(x) 0.44 -0.0011 0.441 -0.00065 0.442 -0.00033 0.443 -0.00011 0.444 -0.000011 0.445 -0.000017 0.446 -0.00013 0.447 -0.00035 0.448 -0.00067 0.449 -0011 0.45 -0.0016 This also was the case with f(x) getting nearer to 0 up until x = 0.444 and then moves away from 0 for x = 0.445.

1. ## Maths - Investigate how many people can be carried in each type of vessel.

We will substitute them back into the equations that we began with. (20 X 8) + (5 X 5) + (10 X 4) = 225 (10 X 8) + (15 X 5)

2. ## 2D and 3D Sequences Project

it to Find the Number of Squares in Higher Sequences I will now prove my equation by applying it to a number of sequences and higher sequences I have not yet explored. Sequence 3: 1. 2(3<sup>2</sup>) - 6 + 1 2. 2(9) - 6 + 1 3. 18 -5 4.

• Over 160,000 pieces
of student written work
• Annotated by
experienced teachers
• Ideas and feedback to