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In a trapezium, when the mid-points of the diagonals are joined, the line so formed is 5 cm long. Further, if the length of one of the parallel sides of the trapezium is 25 cm, then find the length of the other parallel side.
- a)10
- b)15
- c)20
- d)22.5
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
In a trapezium, when the mid-points of the diagonals are joined, the l...
As shown in the figure, the ΔOFE and ΔOAB are similar.
Thus, OF : OA = 5 : 25 = 1 : 5
⇒ OF : AF = 1 : 4
Since, F is the mid-point, therefore AF : FC = 1 : 1 and OF : OC = 1 : 3
Now ΔOFE is similar to ΔOCD
Thus, FE : CD = OF : OC = 1 : 3.
Hence, CD = 3 x 5 = 15 = length of the other parallel side of trapezium.
Thus, OF : OA = 5 : 25 = 1 : 5
⇒ OF : AF = 1 : 4
Since, F is the mid-point, therefore AF : FC = 1 : 1 and OF : OC = 1 : 3
Now ΔOFE is similar to ΔOCD
Thus, FE : CD = OF : OC = 1 : 3.
Hence, CD = 3 x 5 = 15 = length of the other parallel side of trapezium.
Most Upvoted Answer
In a trapezium, when the mid-points of the diagonals are joined, the l...
To solve this problem, let's consider the given trapezium and its properties.
Properties of a Trapezium:
1. A trapezium is a quadrilateral with one pair of parallel sides.
2. The midpoints of the diagonals of a trapezium are collinear.
Given Information:
1. The line formed by joining the midpoints of the diagonals is 5 cm long.
2. The length of one of the parallel sides is 25 cm.
We need to find the length of the other parallel side.
Let's assume the trapezium ABCD, where AB is one of the parallel sides and CD is the other parallel side. Let E and F be the midpoints of AC and BD, respectively.
Length of Line EF:
We are given that the line formed by joining the midpoints of the diagonals is 5 cm long. Let's consider the line EF formed by joining the midpoints E and F.
Thus, EF = 5 cm.
Using the Property of Midpoints:
Since E and F are the midpoints of AC and BD respectively, we can say that EF is parallel and half the length of AD.
Thus, EF = 1/2 * AD.
Length of Line AD:
Let's consider the length of AD as 'a' cm.
Using the Property of Trapezium:
AD is parallel to BC, and EF is parallel to AD.
Therefore, EF is also parallel to BC. Thus, EF is equal to the length of BC, which is 25 cm.
Thus, EF = BC = 25 cm.
Using the Relationship between EF and AD:
We know that EF = 1/2 * AD.
Substituting the values, we get:
5 = 1/2 * a
10 = a
Therefore, the length of AD is 10 cm.
Length of the Other Parallel Side:
We need to find the length of the other parallel side, CD.
Since AD and BC are parallel sides, and AB and CD are parallel sides, we can say that AD = BC and AB = CD.
Therefore, the length of CD is also 10 cm.
Hence, the length of the other parallel side is 10 cm, which corresponds to option B.
Properties of a Trapezium:
1. A trapezium is a quadrilateral with one pair of parallel sides.
2. The midpoints of the diagonals of a trapezium are collinear.
Given Information:
1. The line formed by joining the midpoints of the diagonals is 5 cm long.
2. The length of one of the parallel sides is 25 cm.
We need to find the length of the other parallel side.
Let's assume the trapezium ABCD, where AB is one of the parallel sides and CD is the other parallel side. Let E and F be the midpoints of AC and BD, respectively.
Length of Line EF:
We are given that the line formed by joining the midpoints of the diagonals is 5 cm long. Let's consider the line EF formed by joining the midpoints E and F.
Thus, EF = 5 cm.
Using the Property of Midpoints:
Since E and F are the midpoints of AC and BD respectively, we can say that EF is parallel and half the length of AD.
Thus, EF = 1/2 * AD.
Length of Line AD:
Let's consider the length of AD as 'a' cm.
Using the Property of Trapezium:
AD is parallel to BC, and EF is parallel to AD.
Therefore, EF is also parallel to BC. Thus, EF is equal to the length of BC, which is 25 cm.
Thus, EF = BC = 25 cm.
Using the Relationship between EF and AD:
We know that EF = 1/2 * AD.
Substituting the values, we get:
5 = 1/2 * a
10 = a
Therefore, the length of AD is 10 cm.
Length of the Other Parallel Side:
We need to find the length of the other parallel side, CD.
Since AD and BC are parallel sides, and AB and CD are parallel sides, we can say that AD = BC and AB = CD.
Therefore, the length of CD is also 10 cm.
Hence, the length of the other parallel side is 10 cm, which corresponds to option B.
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In a trapezium, when the mid-points of the diagonals are joined, the line so formed is 5 cm long. Further, if the length of one of the parallel sides of the trapezium is 25 cm, then find the length of the other parallel side.a)10b)15c)20d)22.5Correct answer is option 'B'. Can you explain this answer?
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