CAT 1997 — QA Question 35
Similarity of TrianglesEasy
Passage / Data
Direction: Answer the questions based on the following information.
For these questions the following functions have been defined.
la(x, y, z) = min(x + y, y + z)
le(x, y, z) = max (x − y, y − z)
ma(x, y, z) = [le(x, y, z) + la(x, y, z)]
In ΔABC, points P, Q and R are the mid-points of sides AB, BC and CA respectively. If area of Δ ABC is 20 sq. units, find the area of Δ PQR.
Answer & solution
- A
10 sq.units
- B
5√3 sq. units
5 sq. units
- D
None of these
Solution
In a triangle, the line joining the mid-points of any two sides is half the length of its third side. Hence, every side of ΔPQR would be half the sides of ΔABC. Hence, area of ΔPQR would be the area of ΔABC
× 20 = 5 sq.units