GATE EC 2022 Set 1 — Question 3
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General Aptitude → Quantitative Aptitude → Mensuration & Geometry
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Question
A trapezium has vertices marked as P, Q, R and S (in that order anticlockwise). The side PQ is parallel to side SR.Further, it is given that, , , and .What is the shortest distance between PQ and SR (in cm)?
Correct answer
(B) 2.40
Solution
Let the trapezium be with . Given , , , and .
Draw a line from parallel to that intersects at point .
Then and .
In , the side .
The sides of are , , and .
Since , is a right-angled triangle with the right angle at .
The shortest distance between and is the height () of the trapezium, which is also the altitude of from vertex to the base .
Area of .
Also, Area .
.
Draw a line from parallel to that intersects at point .
Then and .
In , the side .
The sides of are , , and .
Since , is a right-angled triangle with the right angle at .
The shortest distance between and is the height () of the trapezium, which is also the altitude of from vertex to the base .
Area of .
Also, Area .
.
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