To find the perimeter of any shape, we have to add length of all sides.
Perimeter = Sum of known sides + Unknown side
Unknown side = Perimeter - Sum of known sides
Problem 1 :
Solution :
Let, missing side = S
2x² - 5 + 3x² + 9x + S = 5x² + 7x + 12
5x² + 9x – 5 + S = 5x² + 7x + 12
S = 5x² + 7x + 12 – 5x² - 9x + 5
S = - 2x + 17
Problem 2 :
Solution:
Let, missing side = S
7b^{2 }– 2ab + 4a² - 4ab + 9ab + 8a² + S = 9b² - 2ab + 12a²
12a² + 7b² + 3ab + S = 9b² - 2ab + 12a²
S = 9b² - 2ab + 12a² - 12a² - 7b² - 3ab
S = 2b² - 5ab
Problem 3 :
Solution :
Let, missing side = S
2(5x² - 3x + 2) + 2S = 14x² + 4x - 8
10x² - 6x + 4 + 2S = 14x² + 4x - 8
2S = 14x² + 4x – 8 – 10x² + 6x – 4
2S = 4x² + 10x – 12
S = 4x² + 10x – 12
Problem 4 :
The measure of the perimeter of a triangle is 37s + 42. It is known that two of the sides of the triangle have measures of 14s + 16 and 10s + 20. Find the length of the third side.
Solution :
Perimeter of a triangle = 37s + 42
Length of the first side (a) = 14s + 16
Length of the second side (b) = 10s + 20
To find, third side (c)
Perimeter = a + b + c
37s + 42 = 14s + 16 + 10s + 20 + third side
37s + 42 = 24s + 36 + third side
Third side = 37s + 42 – 24s – 36
Third side = 13s + 6
So, the length of the third side is 13s + 6.
Problem 5 :
A triangle has a perimeter of 10a + 3b + 12 and has sides of length 3a + 8 and 5a + b, what is the length of the third side?
Solution :
Perimeter of a triangle = 10a + 3b + 12
Length of the first side = 3a + 8
Length of the second side = 5a + b
To find, third side (c)
Perimeter = a + b + c
10a + 3b + 12 = 3a + 8 + 5a + b + third side
Third side = 10a + 3b + 12 - 3a - 8 - 5a - b
Third side = 2a + 2b + 4
So, the length of the third side is 2a + 2b + 4.
Problem 6 :
For a rectangle with length of 3x + 4 and perimeter of 10x + 18, what is the width of the rectangle?
Solution :
Perimeter of a rectangle = 3x + 4
Length of a rectangle = 3x + 4
Perimeter of a rectangle = 2(l + w)
To find, width (w)
10x + 18 = 2(3x + 4 + w)
10x + 18 = 2(3x + 4) + 2(w)
10x + 18 = 6x + 8 + 2w
2w = 10x + 18 – 6x – 8
2w = 4x + 10
w = (4x + 10) / 2
w = 2x + 5
So, width of the rectangle is 2x + 5.
Problem 7 :
A rectangle has a perimeter of 12y² - 2y + 18 and has a width of 4y² - y + 6. What is the length of the rectangle?
Solution :
Perimeter of a rectangle = 12y² - 2y + 18
Width of a rectangle = 4y² - y + 6
Perimeter of a rectangle = 2(l + w)
To find, length (l)
12y² - 2y + 18 = 2(l + 4y² - y + 6)
12y² - 2y + 18 = 2(l) + 2(4y² - y + 6)
12y² - 2y + 18 = 2l + 8y² - 2y + 12
2l = 12y² - 2y + 18 – 8y² + 2y – 12
2l = 4y² + 6
l = 2y² + 3
So, length of the rectangle is 2y² + 3.
May 21, 24 08:51 PM
May 21, 24 08:51 AM
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