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The perimeter of a trapezium is 58 cm and the sum of its non-parallel sides is 20 cm. If its area is 152 cm2, then the distance between the parallel sides, in cm, is
- a)6
- b)8
- c)9.8
- d)15.2
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
The perimeter of a trapezium is 58 cm and the sum of its non-parallel ...
To solve this problem, we can use the formulas for the perimeter and area of a trapezium.
Given:
Perimeter = 58 cm
Sum of non-parallel sides = 20 cm
Area = 152 cm^2
Let's assume the two parallel sides of the trapezium are a cm and b cm, with a > b. The two non-parallel sides are x cm and y cm, with x + y = 20 cm.
Finding the length of the parallel sides
Using the formula for the perimeter of a trapezium:
Perimeter = a + b + x + y
58 = a + b + x + y
Since x + y = 20 cm, we can rewrite the equation as:
58 = a + b + 20
Rearranging the equation, we get:
a + b = 58 - 20
a + b = 38
Finding the area of the trapezium
Using the formula for the area of a trapezium:
Area = (1/2) * (sum of parallel sides) * (distance between parallel sides)
152 = (1/2) * (a + b) * (distance between parallel sides)
Substituting the value of a + b from the previous equation:
152 = (1/2) * 38 * (distance between parallel sides)
152 = 19 * (distance between parallel sides)
Rearranging the equation, we get:
(distance between parallel sides) = 152/19
(distance between parallel sides) = 8 cm
Therefore, the distance between the parallel sides of the trapezium is 8 cm. Hence, the correct answer is option B.
Given:
Perimeter = 58 cm
Sum of non-parallel sides = 20 cm
Area = 152 cm^2
Let's assume the two parallel sides of the trapezium are a cm and b cm, with a > b. The two non-parallel sides are x cm and y cm, with x + y = 20 cm.
Finding the length of the parallel sides
Using the formula for the perimeter of a trapezium:
Perimeter = a + b + x + y
58 = a + b + x + y
Since x + y = 20 cm, we can rewrite the equation as:
58 = a + b + 20
Rearranging the equation, we get:
a + b = 58 - 20
a + b = 38
Finding the area of the trapezium
Using the formula for the area of a trapezium:
Area = (1/2) * (sum of parallel sides) * (distance between parallel sides)
152 = (1/2) * (a + b) * (distance between parallel sides)
Substituting the value of a + b from the previous equation:
152 = (1/2) * 38 * (distance between parallel sides)
152 = 19 * (distance between parallel sides)
Rearranging the equation, we get:
(distance between parallel sides) = 152/19
(distance between parallel sides) = 8 cm
Therefore, the distance between the parallel sides of the trapezium is 8 cm. Hence, the correct answer is option B.
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Community Answer
The perimeter of a trapezium is 58 cm and the sum of its non-parallel ...
Sum of non-parallel sides is 20 cm and perimeter is 58 cm.
So, sum of parallel sides (2 bases) = 58 - 20 = 38 cm
Area of trapezium = 1/2 × sum of bases × height
Let distance between the parallel sides, i.e., height be H.
So, according to the question,
1/2 × 38 × H = 152
So, H = 8 cm
So, sum of parallel sides (2 bases) = 58 - 20 = 38 cm
Area of trapezium = 1/2 × sum of bases × height
Let distance between the parallel sides, i.e., height be H.
So, according to the question,
1/2 × 38 × H = 152
So, H = 8 cm
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The perimeter of a trapezium is 58 cm and the sum of its non-parallel sides is 20 cm. If its area is 152 cm2, then the distance between the parallel sides, in cm, isa)6b)8c)9.8d)15.2Correct answer is option 'B'. Can you explain this answer?
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