Question

In triangle PQR, S and T are mid points of sides PR and PQ respectively. The medians QS and RT intersect at U. Then area of PQU :area of PQR is -

(a) 1:3
(b) 1:4
(c) 1:5
(d) 2:5​

Answer 1

Given : In triangle PQR, S and T are mid-points of sides PR and PQ respectively,

The medians QS and RT intersect at U.

To Find :  Area of ΔPQU :  Area of ΔPQR

(a) 1:3

(b) 1:4

(c) 1:5

(d) 2:5​

Solution:

S and T are mid-points of sides PR and PQ

QS is median ( median divide triangle in two equal area triangle )

=> Area of ΔPQS = (1/2)Area of ΔPQR

The medians QS and RT intersect at U.

Median intersect Each other  in 2 : 1 ratio from Vertex to base

=> QU : US = 2 : 1

=> Area of ΔPQU = (2/(2 + 1))  Area of ΔPQS

=> Area of ΔPQU = (2/3)  Area of ΔPQS

Area of ΔPQS = (1/2)Area of ΔPQR

=> Area of ΔPQU = (2/3) (1/2)Area of ΔPQR

=> Area of ΔPQU =  (1/3)  Area of ΔPQR

=>  Area of ΔPQU /  Area of ΔPQR = 1/3

=>  Area of ΔPQU :  Area of ΔPQR = 1 : 3

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