Integrated algebra geometry
Introduction :
Algebra is a branch of math’s similar to arithmetic. It deals with processing of calculation. In arithmetic theory, the solutions are found based on the figures, but in algebra the solutions are obtained based on the symbols of algebra. In mathematics, Geometric Algebra is a field relates the algebraic expressions with the geometrical shapes. This kind of mathematics is studied in the field of vectors, complex numbers and etc.
Problems – integrated algebra geometry:
Example 1 - integrated algebra geometry:
A segment of length 90-inches is divided in to three parts by the ratio 6: 5: 4. Find the largest segment.
Solution:
Let us consider 4y be the length of the smallest piece.
5y be the length of the second piece.
Take 6y be the largest piece.
6y + 5y + 4y = 90
15y = 90
y = 6
4y = 4(6) 5y = 5(6) 6y = 6(6)
4y = 24 5y = 30 6y = 36
The length of the largest segment is 36.
Example 2 - integrated algebra geometry:
Find x: if x/2 = 5/4.
Solution:
By property of multiplication,
Using the above property,
(x)(4) = (2) (4)
4x =8
x = 8/4
x = 2.
Problem of similar triangles - Integrated Geometry algebra:
Integrated Geometry algebra Example:
Given that the triangles perimeters are in the ratio of 10: 9. Their sum of the area is given by 905 cm2. Calculate the areas of each similar triangle.
Solution:
Let us consider p and q be two triangles, then
Perimeter of p / perimeter of q = 9/10
Based on integrated Geometry algebra Theorem,
Let 9y = side of p.
And 10y = side of q .
If two triangles are similar, then their areas are x:y.
Area of p / area of q = (x/y)2
Then, area of p / area of q = (9y /10y) 2
=81y2/100y2
Since the total of the areas is 905 cm2, we get
area of p + area of q = 81y2+100y2
905=181y2
y2=5
area of p = 81y2
=81(5)
=405 cm2
area of q = 100y2
=100(5)
=500 cm2
Algebra is a branch of math’s similar to arithmetic. It deals with processing of calculation. In arithmetic theory, the solutions are found based on the figures, but in algebra the solutions are obtained based on the symbols of algebra. In mathematics, Geometric Algebra is a field relates the algebraic expressions with the geometrical shapes. This kind of mathematics is studied in the field of vectors, complex numbers and etc.
Problems – integrated algebra geometry:
Example 1 - integrated algebra geometry:
A segment of length 90-inches is divided in to three parts by the ratio 6: 5: 4. Find the largest segment.
Solution:
Let us consider 4y be the length of the smallest piece.
5y be the length of the second piece.
Take 6y be the largest piece.
6y + 5y + 4y = 90
15y = 90
y = 6
4y = 4(6) 5y = 5(6) 6y = 6(6)
4y = 24 5y = 30 6y = 36
The length of the largest segment is 36.
Example 2 - integrated algebra geometry:
Find x: if x/2 = 5/4.
Solution:
By property of multiplication,
Using the above property,
(x)(4) = (2) (4)
4x =8
x = 8/4
x = 2.
Problem of similar triangles - Integrated Geometry algebra:
Integrated Geometry algebra Example:
Given that the triangles perimeters are in the ratio of 10: 9. Their sum of the area is given by 905 cm2. Calculate the areas of each similar triangle.
Solution:
Let us consider p and q be two triangles, then
Perimeter of p / perimeter of q = 9/10
Based on integrated Geometry algebra Theorem,
Let 9y = side of p.
And 10y = side of q .
If two triangles are similar, then their areas are x:y.
Area of p / area of q = (x/y)2
Then, area of p / area of q = (9y /10y) 2
=81y2/100y2
Since the total of the areas is 905 cm2, we get
area of p + area of q = 81y2+100y2
905=181y2
y2=5
area of p = 81y2
=81(5)
=405 cm2
area of q = 100y2
=100(5)
=500 cm2