Q. 85.0( 1 Vote )

P, Q, R are the mid-points of the sides of ΔABC. X, Y, Z are the mid-points of the sides of ΔPQR. If the area of ΔXYZ is 10, find the area of APQR and the area of ΔABC.

Answer :


In ∆ABC, P, Q, R are the mid-points of the sides AB, BC and CA respectively.



The correspondence ∆ABC∆QRP is a similarity.


Areas of similar triangles are proportional to the squares of their corresponding sides.



∆ABC = ∆POR


Similarly, X,Y and Z are the mid-points of the sides of ∆PQR, we get


∆PQR = 4∆XYZ


∆PQR = 4×10


∆PQR = 40


Thus, the area of ∆PQR is 40 sq. units.


∆ABC = 4∆PQR


∆ABC = 4×40


∆ABC = 160


Hence, the area of ∆ABC is 160 sq. units.


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