Question

in triangle Angle PSR the P is 3o degree and the angle TQR The T is 90 degree and R is x and S is y find the value of x and y​

Answer 1

Answer:

Given:

ST || QR

PT= 4 cm

TR = 4cm

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.

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