Question

In triangle PQR, S and T are two points on PQ and PR respectively.PS=4cm, SQ=3cm, PT=6cm, TR=4.5cm and angle PST=40 degree find angle PQR

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Given :-

• ST || QR

• PT= 4 cm

• TR = 4cm

Solution :-

In ΔPST and ΔPQR ,

∠SPT = ∠QPR (Common)

∠PST = ∠PQR (Corresponding angles)

ΔPST ∼ ΔPQR (By AA similarity criterion)

• We know that the ratio of areas of two similar triangles is equal to the ratio of squares of their corresponding sides.    

                                                         

→ ar(∆PST) /ar(∆PQR) = (PT)²/(PR)²

→ ar(∆PST) /ar(∆PQR) = 4²/(PT+TR)²

→ ar(∆PST) /ar(∆PQR) = 16/(4+4)²= 16/8²=16/64= 1/4

Thus, the ratio of the areas of ΔPST and ΔPQR is 1:4