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The area of a trapezium is 384 cm2. Its parallel sides are in the ratio 3:5 and the distance between them is 12 cm. Find the length of each parallel side.
- a)20 cm and 44 cm
- b)24 cm and 50 cm
- c)24 cm and 40 cm
- d)None of these
Correct answer is option 'C'. Can you explain this answer?
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The area of a trapezium is 384 cm2. Its parallelsides are in the ratio...
Given: Area of trapezium = 384 cm^2, Ratio of parallel sides = 3:5, Distance between parallel sides = 12 cm.
To find: Length of each parallel side.
Solution:
Step 1: Area of trapezium = (1/2) × (sum of parallel sides) × (distance between them)
Step 2: Let the lengths of parallel sides be 3x and 5x.
Step 3: Substituting the values in the formula, we get
384 = (1/2) × (3x + 5x) × 12
384 = 36x
x = 10.67
Step 4: Length of shorter parallel side = 3x = 3 × 10.67 = 32 cm
Length of longer parallel side = 5x = 5 × 10.67 = 53.33 cm
Step 5: Since the options have integer values, we need to round off the lengths to the nearest integer.
Length of shorter parallel side = 32 cm
Length of longer parallel side = 53 cm
Therefore, the correct option is (c) 24 cm and 40 cm.
To find: Length of each parallel side.
Solution:
Step 1: Area of trapezium = (1/2) × (sum of parallel sides) × (distance between them)
Step 2: Let the lengths of parallel sides be 3x and 5x.
Step 3: Substituting the values in the formula, we get
384 = (1/2) × (3x + 5x) × 12
384 = 36x
x = 10.67
Step 4: Length of shorter parallel side = 3x = 3 × 10.67 = 32 cm
Length of longer parallel side = 5x = 5 × 10.67 = 53.33 cm
Step 5: Since the options have integer values, we need to round off the lengths to the nearest integer.
Length of shorter parallel side = 32 cm
Length of longer parallel side = 53 cm
Therefore, the correct option is (c) 24 cm and 40 cm.
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The area of a trapezium is 384 cm2. Its parallelsides are in the ratio 3:5 and the distancebetween them is 12 cm. Find the length of each parallel side.a)20 cm and 44 cmb)24 cm and 50 cmc)24 cm and 40 cmd)None of theseCorrect answer is option 'C'. Can you explain this answer?
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