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The are of a trapezium is 384cm2 if the parallel sides are in the ratio 3:5 and the perpendicular distance between them in 12 cm then find the smaller of the parallel side?
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The are of a trapezium is 384cm2 if the parallel sides are in the rati...
Given Data
- Area of trapezium = 384 cm²
- Ratio of parallel sides = 3:5
- Perpendicular distance between the sides (height) = 12 cm
Understanding the Area of a Trapezium
- The area (A) of a trapezium can be calculated using the formula:
A = (1/2) × (a + b) × h
where a and b are the lengths of the parallel sides, and h is the height.
Expressing Parallel Sides
- Let the lengths of the parallel sides be represented as:
a = 3x (smaller side)
b = 5x (larger side)
- Here, x is a common multiplier based on their ratio.
Substituting into the Area Formula
- Plugging the values into the area formula:
384 = (1/2) × (3x + 5x) × 12
Simplifying the Equation
- Combine the terms:
384 = (1/2) × (8x) × 12
384 = 48x
- Solving for x:
x = 384 / 48
x = 8
Finding the Lengths of Parallel Sides
- Now, substitute x back into the expressions for a and b:
a = 3x = 3 × 8 = 24 cm
b = 5x = 5 × 8 = 40 cm
Conclusion
- The smaller parallel side of the trapezium is 24 cm.
- Area of trapezium = 384 cm²
- Ratio of parallel sides = 3:5
- Perpendicular distance between the sides (height) = 12 cm
Understanding the Area of a Trapezium
- The area (A) of a trapezium can be calculated using the formula:
A = (1/2) × (a + b) × h
where a and b are the lengths of the parallel sides, and h is the height.
Expressing Parallel Sides
- Let the lengths of the parallel sides be represented as:
a = 3x (smaller side)
b = 5x (larger side)
- Here, x is a common multiplier based on their ratio.
Substituting into the Area Formula
- Plugging the values into the area formula:
384 = (1/2) × (3x + 5x) × 12
Simplifying the Equation
- Combine the terms:
384 = (1/2) × (8x) × 12
384 = 48x
- Solving for x:
x = 384 / 48
x = 8
Finding the Lengths of Parallel Sides
- Now, substitute x back into the expressions for a and b:
a = 3x = 3 × 8 = 24 cm
b = 5x = 5 × 8 = 40 cm
Conclusion
- The smaller parallel side of the trapezium is 24 cm.
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The are of a trapezium is 384cm2 if the parallel sides are in the ratio 3:5 and the perpendicular distance between them in 12 cm then find the smaller of the parallel side?
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The are of a trapezium is 384cm2 if the parallel sides are in the ratio 3:5 and the perpendicular distance between them in 12 cm then find the smaller of the parallel side? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The are of a trapezium is 384cm2 if the parallel sides are in the ratio 3:5 and the perpendicular distance between them in 12 cm then find the smaller of the parallel side? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The are of a trapezium is 384cm2 if the parallel sides are in the ratio 3:5 and the perpendicular distance between them in 12 cm then find the smaller of the parallel side?.
The are of a trapezium is 384cm2 if the parallel sides are in the ratio 3:5 and the perpendicular distance between them in 12 cm then find the smaller of the parallel side? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The are of a trapezium is 384cm2 if the parallel sides are in the ratio 3:5 and the perpendicular distance between them in 12 cm then find the smaller of the parallel side? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The are of a trapezium is 384cm2 if the parallel sides are in the ratio 3:5 and the perpendicular distance between them in 12 cm then find the smaller of the parallel side?.
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