Introduction for geometry:
Geometry is one of the main branch of mathematics. The word “geometry” is resultant from the combination of two Greek words “geo” and “metron”. geo means “earth” and metron means “measurement”. ”Euclid, a distinguished Greek mathematician, called the father of geometry. A point is used to represent a place in space. a plane to be a surface extending infinitely in all directions such that all points lying on the line joining any two points on the surface.
Example problems for geometry:
Example 1:
Solving the following equation, Calculate the values for x-intercept, the y-intercept, and the slope .
2x + 4y = 20
Solution:
The slope intercept form, y= mx +b
Here m represent slope
b represent y intercept
2x+4y=20
On solving this, We get
4y = 20-2x
4y = -2x+20
On solving this, We get
y = (-2/4) x+20/4
y = (-1/2) x+5
X-intercept = 5
Y-intercept = 5
Slope = - 0.5
Example 2:
John wants to decorate her Christmas tree. He wants to place the tree on a greeting box covered with colored paper with picture of Santa Claus on it. He must know the correct quantity of paper buying for this purpose. If the box has length, breadth and height as 60 cm, 20 cm and 10 cm respectively how many square sheets of paper of side 10 cm would he need?
Solution:
Since John wants to paste the paper on the outer surface of the box, the quantity of paper required would be equal to the surface area of the box, which is of the shape of cuboids. The dimensions of the box are:
Length =60 cm, Breadth = 20 cm, Height = 10 cm.
The surface area of the box = 2( lb + bh + hl )
= 2[(60 × 20) + (20 × 10) + (10 × 60)] cm^2
On solving this, We get
= 2(1200 + 200 + 600) cm^2
= 2 × 2000 cm^2 = 4000 cm^2
The area of each sheet of the paper = 10 × 10 cm^2
= 1000 cm^2
Therefore, the required sheet = surface area of box/ area of one sheet of paper
= 4000/1000
On solving this, We get
= 4
Therefore, he would need for 4 sheets.
Is this topic Completing the Square Formula hard for you? Watch out for my coming posts.
Practice problems for geometry:
Practice problem 1: Determine the slope of the line whose equation is 3x + 4y = 12 and whose y-intercept is (0,5)
Ans: m = -3/4
Practice problem 2: The two angle is 40° , 56° , Find the third angle of triangle.
Ans: 84°
Practice problem 3: What is the complementary angle of 39°
Ans: 51°
Practice problem 4: Find the slope of the line whose equation is 3x + 4y + 5 = 0.
Ans: m = - 3/4 , c = -5/4
Geometry is one of the main branch of mathematics. The word “geometry” is resultant from the combination of two Greek words “geo” and “metron”. geo means “earth” and metron means “measurement”. ”Euclid, a distinguished Greek mathematician, called the father of geometry. A point is used to represent a place in space. a plane to be a surface extending infinitely in all directions such that all points lying on the line joining any two points on the surface.
Example problems for geometry:
Example 1:
Solving the following equation, Calculate the values for x-intercept, the y-intercept, and the slope .
2x + 4y = 20
Solution:
The slope intercept form, y= mx +b
Here m represent slope
b represent y intercept
2x+4y=20
On solving this, We get
4y = 20-2x
4y = -2x+20
On solving this, We get
y = (-2/4) x+20/4
y = (-1/2) x+5
X-intercept = 5
Y-intercept = 5
Slope = - 0.5
Example 2:
John wants to decorate her Christmas tree. He wants to place the tree on a greeting box covered with colored paper with picture of Santa Claus on it. He must know the correct quantity of paper buying for this purpose. If the box has length, breadth and height as 60 cm, 20 cm and 10 cm respectively how many square sheets of paper of side 10 cm would he need?
Solution:
Since John wants to paste the paper on the outer surface of the box, the quantity of paper required would be equal to the surface area of the box, which is of the shape of cuboids. The dimensions of the box are:
Length =60 cm, Breadth = 20 cm, Height = 10 cm.
The surface area of the box = 2( lb + bh + hl )
= 2[(60 × 20) + (20 × 10) + (10 × 60)] cm^2
On solving this, We get
= 2(1200 + 200 + 600) cm^2
= 2 × 2000 cm^2 = 4000 cm^2
The area of each sheet of the paper = 10 × 10 cm^2
= 1000 cm^2
Therefore, the required sheet = surface area of box/ area of one sheet of paper
= 4000/1000
On solving this, We get
= 4
Therefore, he would need for 4 sheets.
Is this topic Completing the Square Formula hard for you? Watch out for my coming posts.
Practice problems for geometry:
Practice problem 1: Determine the slope of the line whose equation is 3x + 4y = 12 and whose y-intercept is (0,5)
Ans: m = -3/4
Practice problem 2: The two angle is 40° , 56° , Find the third angle of triangle.
Ans: 84°
Practice problem 3: What is the complementary angle of 39°
Ans: 51°
Practice problem 4: Find the slope of the line whose equation is 3x + 4y + 5 = 0.
Ans: m = - 3/4 , c = -5/4
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