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A park is shaped like a rhombus and has area 96 sq m. If 40 m of fencing is needed to enclose the park, the cost, in INR, of laying electric wires along its two diagonals, at the rate of ₹125 per m, is
Correct answer is '3500'. Can you explain this answer?
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A park is shaped like a rhombus and has area 96 sq m. If 40 m of fenci...
We can say 40m is the perimeter of the park
so side of rhombus = 10
And as we know diagonals of a rhombus are perpendicular bisectors of each other :
Solving (1) and (2)
Now the cost, in INR, of laying electric wires along its two diagonals, at the rate of ₹125 per m, is= (12+16)(125) =3500
so side of rhombus = 10
And as we know diagonals of a rhombus are perpendicular bisectors of each other :
Solving (1) and (2)
Now the cost, in INR, of laying electric wires along its two diagonals, at the rate of ₹125 per m, is= (12+16)(125) =3500
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A park is shaped like a rhombus and has area 96 sq m. If 40 m of fenci...
Understanding the Problem
To solve the problem, we need to determine the lengths of the diagonals of the rhombus and then compute the cost of laying electric wires along these diagonals.
Area of the Rhombus
- The area (A) of a rhombus can be calculated using the formula:
A = (d1 * d2) / 2
where d1 and d2 are the lengths of the diagonals.
- Given that the area is 96 sq m:
d1 * d2 = 192
Perimeter and Diagonal Relationship
- The perimeter (P) of a rhombus is given by:
P = 4 * side length
Given P = 40 m:
side length = 40 / 4 = 10 m
- The relationship between the sides and the diagonals in a rhombus is:
side^2 = (d1/2)^2 + (d2/2)^2
- Substituting the side length:
10^2 = (d1/2)^2 + (d2/2)^2
100 = (d1^2 + d2^2) / 4
Therefore, d1^2 + d2^2 = 400
Solving for Diagonal Lengths
- We have two equations:
1. d1 * d2 = 192
2. d1^2 + d2^2 = 400
- Let d1 = x and d2 = 192/x.
Substitute into the second equation and solve for x, yielding d1 and d2.
Cost Calculation
- Once the lengths of the diagonals are found, the total length for electric wiring is:
Total length = d1 + d2.
- Finally, calculate the cost:
Cost = Total length * Rate
Cost = (d1 + d2) * 125
After solving, the correct cost of laying electric wires is INR 3500.
To solve the problem, we need to determine the lengths of the diagonals of the rhombus and then compute the cost of laying electric wires along these diagonals.
Area of the Rhombus
- The area (A) of a rhombus can be calculated using the formula:
A = (d1 * d2) / 2
where d1 and d2 are the lengths of the diagonals.
- Given that the area is 96 sq m:
d1 * d2 = 192
Perimeter and Diagonal Relationship
- The perimeter (P) of a rhombus is given by:
P = 4 * side length
Given P = 40 m:
side length = 40 / 4 = 10 m
- The relationship between the sides and the diagonals in a rhombus is:
side^2 = (d1/2)^2 + (d2/2)^2
- Substituting the side length:
10^2 = (d1/2)^2 + (d2/2)^2
100 = (d1^2 + d2^2) / 4
Therefore, d1^2 + d2^2 = 400
Solving for Diagonal Lengths
- We have two equations:
1. d1 * d2 = 192
2. d1^2 + d2^2 = 400
- Let d1 = x and d2 = 192/x.
Substitute into the second equation and solve for x, yielding d1 and d2.
Cost Calculation
- Once the lengths of the diagonals are found, the total length for electric wiring is:
Total length = d1 + d2.
- Finally, calculate the cost:
Cost = Total length * Rate
Cost = (d1 + d2) * 125
After solving, the correct cost of laying electric wires is INR 3500.
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A park is shaped like a rhombus and has area 96 sq m. If 40 m of fencing is needed to enclose the park, the cost, in INR, of laying electric wires along its two diagonals, at the rate of 125 per m, isCorrect answer is '3500'. Can you explain this answer?
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A park is shaped like a rhombus and has area 96 sq m. If 40 m of fencing is needed to enclose the park, the cost, in INR, of laying electric wires along its two diagonals, at the rate of 125 per m, isCorrect answer is '3500'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A park is shaped like a rhombus and has area 96 sq m. If 40 m of fencing is needed to enclose the park, the cost, in INR, of laying electric wires along its two diagonals, at the rate of 125 per m, isCorrect answer is '3500'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A park is shaped like a rhombus and has area 96 sq m. If 40 m of fencing is needed to enclose the park, the cost, in INR, of laying electric wires along its two diagonals, at the rate of 125 per m, isCorrect answer is '3500'. Can you explain this answer?.
A park is shaped like a rhombus and has area 96 sq m. If 40 m of fencing is needed to enclose the park, the cost, in INR, of laying electric wires along its two diagonals, at the rate of 125 per m, isCorrect answer is '3500'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A park is shaped like a rhombus and has area 96 sq m. If 40 m of fencing is needed to enclose the park, the cost, in INR, of laying electric wires along its two diagonals, at the rate of 125 per m, isCorrect answer is '3500'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A park is shaped like a rhombus and has area 96 sq m. If 40 m of fencing is needed to enclose the park, the cost, in INR, of laying electric wires along its two diagonals, at the rate of 125 per m, isCorrect answer is '3500'. Can you explain this answer?.
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