Introduction to geometric word problems:
Geometry is a theoretical subject, but easy to learn, and it has many real practical applications. Finally, geometry has developed into a skillfully arranged and sensibly organized body of knowledge.
Geometry gives the planning of different geometrical shapes and figures in our daily life such as articles in the houses, wells, buildings, bridges etc. The term 'Geometry' means a study (learn) of properties of figures and shapes and the relationship between them.
Example problems of geometric word problems:
Geometric word problem 1:
Find the largest possible rectangular area we can enclose, assuming we have 144 centimeters of fencing. What is the implication of the dimensions of this largest possible enclosure?
Geometric word problem Solution:
Let the length be L and the width be W. We have 144 centimeters of fencing, so the perimeter equation is:
2L + 2W = 144
Dividing by 2 to make things simpler, then we get
L + W = 72
Area of the rectangle formula as,
A = L × W
We can substitute for either one of the above variables by solving the perimeter equation:
L + W = 72
L = 72 – W
Then we get,
A = (72 – W) × W
= 72W – W 2
This equation is in the format of ax2+bx+c.
A = –W 2 + 72W
The vertex of a parabola is the point (h, k), where h = –b/2a. In this case:
h = –(72)/(2×(–1)) = 36
To find the "k" part of the vertex, all we do is plug 36 in for W:
k = –(36)2 + 72(36) = 3888
The largest possible area is 3888 square centimeters
Now w e can find the length by using the value of width. Then we get,
L = 72– W = 72 – 36 = 36
Then the length and width are the same: 36 centimeters.
Therefore, the largest possible rectangular area is in the shape of a square.
Geometric word problem 2:
A square has an area of twenty five square centimeters. What is the length of each of its sides?
Geometric word problem Solution:
The formula for the area A of a square with side-length ‘a’ is:
A = a2
Substitute the value of A in the above formula: Then we get,
25= a2
√25 = a
5 = a
After re-reading,
a=5 cm
The length of each side is 5 centimeters.
Practice geometric word problems:
A circle has an area of 81π square units. What is the length of the circle's diameter?
Answer: 9
A piece of 16-gauge copper wire 54 cm long is twisted into the shape of a rectangle whose width is twice its length. Find the dimensions of the rectangle.
Answer: L=9 cm and W=18 cm
Geometry is a theoretical subject, but easy to learn, and it has many real practical applications. Finally, geometry has developed into a skillfully arranged and sensibly organized body of knowledge.
Geometry gives the planning of different geometrical shapes and figures in our daily life such as articles in the houses, wells, buildings, bridges etc. The term 'Geometry' means a study (learn) of properties of figures and shapes and the relationship between them.
Example problems of geometric word problems:
Geometric word problem 1:
Find the largest possible rectangular area we can enclose, assuming we have 144 centimeters of fencing. What is the implication of the dimensions of this largest possible enclosure?
Geometric word problem Solution:
Let the length be L and the width be W. We have 144 centimeters of fencing, so the perimeter equation is:
2L + 2W = 144
Dividing by 2 to make things simpler, then we get
L + W = 72
Area of the rectangle formula as,
A = L × W
We can substitute for either one of the above variables by solving the perimeter equation:
L + W = 72
L = 72 – W
Then we get,
A = (72 – W) × W
= 72W – W 2
This equation is in the format of ax2+bx+c.
A = –W 2 + 72W
The vertex of a parabola is the point (h, k), where h = –b/2a. In this case:
h = –(72)/(2×(–1)) = 36
To find the "k" part of the vertex, all we do is plug 36 in for W:
k = –(36)2 + 72(36) = 3888
The largest possible area is 3888 square centimeters
Now w e can find the length by using the value of width. Then we get,
L = 72– W = 72 – 36 = 36
Then the length and width are the same: 36 centimeters.
Therefore, the largest possible rectangular area is in the shape of a square.
Geometric word problem 2:
A square has an area of twenty five square centimeters. What is the length of each of its sides?
Geometric word problem Solution:
The formula for the area A of a square with side-length ‘a’ is:
A = a2
Substitute the value of A in the above formula: Then we get,
25= a2
√25 = a
5 = a
After re-reading,
a=5 cm
The length of each side is 5 centimeters.
Practice geometric word problems:
A circle has an area of 81π square units. What is the length of the circle's diameter?
Answer: 9
A piece of 16-gauge copper wire 54 cm long is twisted into the shape of a rectangle whose width is twice its length. Find the dimensions of the rectangle.
Answer: L=9 cm and W=18 cm
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