Question

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 ΔPQR and the area of ΔABC.

Answer 1

Answer:

Area of ∆ABC is 40 and Area of ∆PQR is 160

Answer 2

Answer:

∆PQR = 40

∆ABC = 160

Step-by-step explanation:

In this question,

P,Q,R are the midpoints of sides of ∆ABC. X,Y,Z are the midpoints of the sides of ∆PQR. If area of ∆XYZ ia 10.

Find the area of ∆PQR and area of ∆ABC?

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 = ∆PQR

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.