Answers
Answer:
Total cost will be 7500 rupees.
Step-by-step explanation:
Given:-
Cost of cementing the path = 7500 m².
Dimensions of the rectangular field are:-
Length of the rectangular field(l) = 80m
Breath of the rectangular field(b) = 60m
Width of the path = 5m
Refer to the diagram above to understand the question properly.
Area of the inner rectangular field
=> l× b
=> 80 × 60m²
=> 4800m²
When the path are joined then the length of the outer rectangular field will be
=> 80m + (5 + 5)m
=> 90m
Breath of the outer rectangular field
=> 60m + (5 + 5)m
=> 70m
Area of the outer rectangular field
=> l × b
=> 90 × 70m²
=> 6300m²
Area of the path will be
= Area of rectangular field - Area of inner rectangular field
=> 6300m² - 4800m²
=> 1500m²
Also we have:-
Cost of cementing 1 m² = 5 rupees
Cost of cementing 1500m² = 1500 × 5 rupees
Cost of cementing 1500m² = 7500 rupees
Therefore:-
Total cost will be 7500 rupees.
#answerwithquality #BAL
Answer:
Refer to attachment for figure
Let the breadth of the rectangular field be x m
Length of the rectangular field = 3 times the breadth = 3 * x = 3x m
Area of the rectangular field = Length * Breadth = 3x * x = 3x² m²
Given
A Path 5m wide runs along inside a rectangular field.
Therefore find the dimenisions and area of rectangular field when path is not included
Width of the path = 5 m
Length of the rectangular field when path is not included = 3x - 2(Width of the path) = 3x - 2(5) = 3x - 10 = (3x - 10) m
Breadth of the rectangular field when path is not included = x - 2(Width of the path) = x - 2(5) = x - 10 = (x - 10) m
Area of the rectangular field when path is not included = Length * Breadth
= (3x - 10)(x - 10)
= 3x(x - 10) - 10(x - 10)
= 3x² - 30x - 10x + 100
= 3x² - 40x + 100
Given
Area of the path = 500 m²
i.e Area of the rectangular field - Area of the rectangular field when path is not included = 500 m²
\implies 3 {x}^{2} - (3 {x}^{2} - 40x + 100) = 500⟹3x2−(3x2−40x+100)=500
\implies 3 {x}^{2} - 3 {x}^{2} + 40x - 100 = 500⟹3x2−3x2+40x−100=500
\implies 40x - 100 = 500⟹40x−100=500
\implies 40x - 100 = 500⟹40x−100=500
\implies 40x = 500 + 100⟹40x=500+100
\implies 40x = 600⟹40x=600
\implies 4x = 60⟹4x=60
\implies x = \dfrac{60}{4}⟹x=460
\implies \boxed{x = 15}⟹x=15
Breadth of the rectangle = x = 15 m
Length of the rectangle = 3x = 3 * 15 = 45 m
Hence, length and breadth of the field are 45 m and 15 m respectively.