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CAT 1997 — QA Question 43

Basics of QuadrilateralsEasy

In the given figure, EADF is a rectangle and ABC is a triangle whose vertices lie on the sides of EADF and AE = 22, BE = 6, CF = 16 and BF = 2. Find the length of the line joining the mid-points of the sides AB and BC.

Answer & solution

Correct answer: 5

  • A

    4√2

  • 5

  • C

    3.5

  • D

    None of these

Solution

We know that length of the line joining the mid-points of two sides of a triangle is half the length of third side. Hence, the required length is half the length of side AC. Since EADF is rectangle, EF = AD = 8.
CD = (22 – 16) = 6.
So in the right-angled ΔADC, AD = 8 and CD = 6.
Therefore, AC = 10. Hence, length of the line joining the mid-points of AB and BC = 12(10) = 5.

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CAT 1997 QA Q43: In the given figure, EADF is a rectangle and ABC is a triangle whose vertices lie on the sides of EADF and AE — Solution | TheCATExam